Answer:
Option D - [tex]\frac{2}{7}[/tex].
Step-by-step explanation:
Given : From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event.
To find : What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?
Solution :
Choosing 4 people out of 8 volunteers is [tex]^8C_4[/tex]
[tex]^8C_4=\frac{8!}{4!(8-4)!}[/tex]
[tex]^8C_4=\frac{8\times 7\times 6\times 5\times 4!}{4!\times 4\times 3\times 2}[/tex]
[tex]^8C_4=70[/tex]
Choosing a group of 4 with Andrew and no karein is given by,
One position is fixed by Andrew and Karein the number of volunteer left is 6.
Rest 3 volunteers is chosen from 6.
Choosing 3 people out of 6 volunteers is [tex]^6C_3[/tex]
[tex]^6C_3=\frac{6!}{3!(6-3)!}[/tex]
[tex]^6C_3=\frac{6\times 5\times 4\times 3!}{3!\times 3\times 2}[/tex]
[tex]^6C_3=20[/tex]
The probability that Andrew will be among the 4 volunteers selected and Karen will not is given by,
[tex]P=\frac{^6C_3}{^8C_4}[/tex]
[tex]P=\frac{20}{70}[/tex]
[tex]P=\frac{2}{7}[/tex]
The probability that Andrew will be among the 4 volunteers selected and Karen will not is [tex]\frac{2}{7}[/tex].
Therefore, option D is correct.
write the slope-intercept form of the equation for the line that passes through (4,9) and is parallel to the graph of the equation 5x-4y=8
Answer:
y=1.25x+4
Step-by-step explanation:
Two equations are paralell if they have the same slope.Then to find the paralell equation to [tex]5x-4y=8[/tex], we can do the following: clear out y as a function of x, to get the intercept and the slope that accompanies x.To do this, we follow the next steps: 1) subtract 5x both sides of the equation (which results in [tex]-4y=8-5x[/tex]; 2) divide both sides by (-4), would yield [tex]y=1.25x-2[/tex].Now we have an clear expression of y as a function of x, and can find a parallel line that passes through (x,y)=(4,9). This new equation shall be an expression that meets the following: 9=1.25 (4)+h, where we do not know the value of h, and the values of (x,y) have been replaced by the point required.If we solve the equation above, we obtain the value of h (intercept) for our parallel equation: h=4.Then, the parallel equation that passes through (4,9) is y=1.25x+4 (to verify this is ok, replace x=4 in this equation, and you will get y=9, which is what we were lloking for: a parallel equation to y=1.25x-2 that passes through (4,9)Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used? ∠ABC ≅ ∠BAC; corresponding angles of parallel lines are congruent. ∠CAB ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ACD ≅ ∠ABD; corresponding angles of parallel lines are congruent.
Answer:
C
Step-by-step explanation:
The true statement is that proves the congruence of both triangles is:
∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent How to prove that angles are congruentFrom the complete question, we have the following highlights
Angles B and C are alternate interior anglesThe triangles are bounded by parallel linesThe above highlights mean that:
Angles ABC and DCB are congruent, by the theorem of alternate interior angles of parallel lines
Hence, the true statement is (c)
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This past weekend Miss Thomas did some hallelujah shopping. She bought three presents and says that she has 30% of her shopping finished. How many presents does she have left to purchase?
Answer: the number of presents that she has left to purchase is 6
Step-by-step explanation:
Let x represent the total number of presents that she has to purchase.
She bought three presents and says that she has 30% of her shopping finished. This means that she has finished (1/3 × x) = x/3 shopping. This is equivalent to 3 presents. Therefore,
x/3 = 3
x = 3×3 =9
She had 9 shopping to do
The number of shopping left will be total shopping that she has to do minus the shopping that she has done. It becomes
9 - 3 = 6
The number of surface flaws in a plastic roll used for auto interiors follows a Poisson distribution with a mean of 0.05 flaw per square foot . Each car contains 10 ft2 of the plastic roll and ten (10) of the cars are sold to a particular rental agency. a) What is the probability that there are no flaws in a given car’s interior
Answer:
0.6065
Step-by-step explanation:
Probability mass function of probability distribution : [tex]P(X=x)=\frac{e^{-\lambda} \times \lambda^x}{x !}[/tex]
a mean of 0.05 flaw per square foot
Each car contains 10 sq.feet of the plastic roll
Mean = 0.05
Mean = [tex]\lambda = 0.05 \times 10=0.5[/tex]
We are supposed to find What is the probability that there are no flaws in a given car’s interior i.e,P(X=0)
Substitute the value in the formula
[tex]P(X=0)=\frac{e^{-0.5} \times (0.5)^0x}{0 !}[/tex]
[tex]P(X=0)=\frac{e^{-0.5} \times (0.5)^0}{1}[/tex]
[tex]P(X=0)=0.6065[/tex]
Hence the probability that there are no flaws in a given car’s interior is 0.6065
The price of an item yesterday was $140. Today, the price fell to $91. Find the percentage decrease.
Answer:
65% decrease
Step-by-step explanation:
65% of 140 = 91
Answer:
The price of an item yesterday was $140. Today, the price fell to $91. The percentage decrease is 35%
Explanation:
To find the percentage decrease of a number we first find the difference between the two given numbers, this difference is called the decrease.So we are given a decrease from $140 to $91 ,
the difference = 140 - 91 = 49
Now to find percent decrease we first divide the difference with the original number i.e 140 and
[tex]\frac{49}{140}=0.35[/tex]
[tex]0.35 \times 100[/tex] = 35%
which is the value of percentage decrease.
The box of a well-known breakfast cereal states that one ounce of the cereal contains 113 Calories (1 food Calorie = 4186 J). If 2.51% of this energy could be converted by a weight lifter's body into work done in lifting a barbell, what is the weight of the heaviest barbell that could be lifted a distance of 2.12 m?
Answer:
F = 49,56 Kgs
Step-by-step explanation:
We Know that 113 calories = 4186 J
Joules ( energy unit in MKS system meter, kilograms , second)
and 2,51 % of 4186 is 0,0251 * 4186 = 105.07 J
That the energy available
Work is W = F * d
where F is the force you have to apply and d is traveled distance
in this case F is the weight of the barbell
Then
F = W / d ⇒ F = 105.7 / 2.12 ⇒ F = 49,56 Kgs
Auto insurance Insurance companies collect annual pay-ments from drivers in exchange for paying for the cost of accidents.a) Why should you be reluctant to accept a $1500 pay-ment from your neighbor to cover his automobile accidents in the next year?b) Why can the insurance company make that offer
Answer:
Step-by-step explanation:
a) Because you are only receiving $1500 and in exchange you would have to cover for this accident damage in the next year, which could be up to hundred of thousands of dollar. Sure there's a chance the your neighbor might drive safely, but the odds are far more in his favor than yours.
b) The insurance company collect payments from hundred of thousands buyers, making their cash flow up to tens of million dollar. Sure the expected value of accidents might be high but as a company they surely have capital to cover a handful of cases, if their calculation done right.
Final answer:
One should be reluctant to accept a $1500 payment to cover a neighbor's car accidents due to the potential for costs to exceed this amount. Insurance companies, with their risk-pooling model, accumulate enough in premiums to cover accidents across a large customer base and manage risk effectively.
Explanation:
You should be reluctant to accept a $1500 payment from your neighbor to cover his automobile accidents for the next year because the cost of a potential accident could far exceed the amount collected. If your neighbor is involved in an accident, the resulting expenses for vehicle repairs, medical bills, or other damages could be much greater than $1500, leaving you responsible for the remainder of the costs.
On the other hand, an insurance company can make such an offer because they operate on a system of pooled risk. If each of the 100 drivers pays a $1,860 premium each year, the insurance company will collect a total of $186,000. This amount is calculated to cover the expected costs of accidents across their entire customer base, using statistics and probability to spread the risk among many policyholders. While some drivers may have no accidents, others may have expensive claims, but the total premiums collected can cover the aggregate cost of the accidents that occur.
Additionally, insurance companies can classify people into risk groups and adjust the premiums accordingly. For example, drivers with a good driving record may pay less than those with a history of accidents. This allows the company to minimize their risk while ensuring that those who are less likely to file a claim aren't subsidizing those with higher risks.
Parallelograms ABCD and EFGH are similar figures because angles A, B, C, and D are congruent to angles E, F, G, and H, respectively. If DA equals 8 units, AB equals 11 units, and HE equals 32 units, what does EF equal?
Answer:
It is 44
Step-by-step explanation:
Devon wants to memorize 1/2 of his lines for a play by the end of the week.He has already memorized 1/8 of his lines.what fraction of his lines does he still have left to memorize? Draw a visual model to support answer
Answer:
3/8 left
Step-by-step explanation:
I can't draw a model but I can still give an explanation.
1/2 required to memorize - 1/8 already memorized = 3/8 left
Maybe draw a rectangle with 8 divisions and label the situation.
Devon still needs to memorize 3/8 of his lines. This is determined by converting 1/2 to 4/8 and then subtracting the 1/8 he's already learned, leaving 3/8 of his lines remaining.
Explanation:Devon aims to memorize 1/2 of his lines and has already memorized 1/8 of them. The task here is to find out how many more lines Devon has left to learn. In terms of fractions, this would involve subtracting the already learnt fraction (1/8) from the total goal (1/2).
Firstly, make sure both fractions have the same denominator, for easy calculation. In this case, you can convert 1/2 to 4/8. Now, subtract what you've already learnt. So 4/8 - 1/8 equals 3/8. That means Devon has 3/8 of his lines left to memorize.
To illustrate this visually, consider a pie representing all of Devon's lines. Cut it into 8 even slices. Four of these slices represent the half that Devon wants to learn. He has already learnt one slice (1/8 of the pie). So, he has three slices (3/8 of the pie) left to learn.
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If a total are of the chessboard is 144 square inches. What is the area of one shaded square. What is the total area of all the shaded squares and total area of all the white squares.
Answer: The area of one shaded square is 1 inch^2
The total area of all the shaded squares is 144/2 = 72 inches square
The total area of all the white squares is also 72 inches square
Step-by-step explanation:
If a total area of the chessboard is 144 square inches. The length of both sides are equal because it is a square. The formula for area is length ^2
The length of one side = √area
The length of one side = √144 = 12 inches
This means that both sides of the chessboard is 12 inches. Each side is divided into 12 partitions measuring 1 inch each. This forms a smaller square whose area is
1 inch by 1 inch. Therefore,
The area of one shaded square is
1 inch^2
The total area of the white squares and the shaded squares is 144. Therefore,
The total area of all the shaded squares is 144/2 = 72 inches square
The total area of all the white squares is also 72 inches square
A model for the density δ of the earth’s atmosphere near its surface isδ=619.09−0.000097pwhere p (the distance from the center of the earth) is measured in meters and δ is measured in kilograms per cubic meter. If we take the surface of the earth to be a sphere with radius 6370 km, then this model is a reasonable one for:6.370×106≤p≤6.375×106 Use this model to estimate the mass of the atmosphere between the ground and an altitude of 5 km.
Final answer:
The mass of the Earth's atmosphere from the surface up to an altitude of 5 km can be estimated by integrating the given density model over the surface area of a spherical shell between the radii corresponding to the Earth's surface and the 5 km altitude.
Explanation:
We will use the given model for the density of the Earth's atmosphere near the surface, δ = 619.09 - 0.000097p, to estimate the mass of the atmosphere up to an altitude of 5 km. The radius of the Earth is 6370 km, which is 6.370×106 meters. The altitude of 5 km is 5,000 meters, so we are considering the range of p from 6.370×106 meters to 6.370×106 meters + 5,000 meters.
To estimate the mass of the atmosphere between these two altitudes, we need to integrate the density function δ(p) over the surface area of the sphere at each value of p. For a thin spherical shell, the volume dV is given by the surface area 4πp2 times a small change in radius dp. Therefore, the mass dm contained in a shell is δ(p) * 4πp2 * dp.
To find the total mass, we integrate this expression between the two radii, resulting in:
M = ∫ 6.370×1066.375×106 δ(p) * 4πp2 * dp
Upon performing this integration, we would obtain the estimated total mass of the atmosphere between the ground level and 5 km of altitude.
integral_(6.37×10^6)^(6.375×10^6) (619.09 - 0.000097 p) 4 (π p)^2 dp = 767*10^18
university administrators are becoming more and more alarmed at the number of hours students work per week while attending the university. To study this issue, one administrator was assigned to examine the relationship between the number of hours worked per week in a semester and that semester's GPA for a random sample of students.In this study, what is the explanatory variable?
Answer:
The number of hours worked per week
Step-by-step explanation:
To study this issue, one administrator was assigned to examine the relationship between the number of hours worked per week in a semester and that semester's GPA for a random sample of students.
Here the explanatory variable is - the number of hours worked per week.
An explanatory variable or also called an independent variable, is the variable that is manipulated by the researcher based on the variations in the response variable of an experimental study.
Find the lateral surface of the prism
Answer: [tex]LSA=128\ cm^2[/tex]
Step-by-step explanation:
The formula for calcualte the Lateral surface area of a prism is:
[tex]LSA=Ph[/tex]
Where "P" is the perimeter of the base and "h" is the height of the prism.
Notice that the base is a triangle. Since the perimeter is the sum of its sides, you get that this is:
[tex]P=5\ cm+6\ cm+5\ cm\\\\P=16\ cm[/tex]
You can identify in the figure that the height is:
[tex]h=8\ cm[/tex]
Therefore, you can substitute these values into the formula in order to calculate the Lateral surface area of the given prism. This is:
[tex]LSA=(16\ cm)(8\ cm)\\\\LSA=128\ cm^2[/tex]
Answer:
128
Step-by-step explanation:
A cattle rancher is going to sell one of his prize bulls at an auction and would like to make $36,400 after paying a 9% commission to the auctioneer. For what selling price will the rancher make this amount of money?
Answer:
$40,000
Step-by-step explanation:
Let x represent the selling price of the bull.
We have been given that a cattle rancher would like to make $36,400 after paying a 9% commission to the auctioneer.
The commission would be 9% of selling price, that is [tex]\frac{9}{100}x=0.09x[/tex].
The profit of the rancher can be counted after paying off the commission that would be [tex]x-0.09x[/tex].
Since rancher wants to make $36,400 after paying a 9% commission, so we can represent this information in an equation as:
[tex]x-0.09x=36,400[/tex]
[tex]0.91x=36,400[/tex]
[tex]\frac{0.91x}{0.91}=\frac{36,400}{0.91}[/tex]
[tex]x=40,000[/tex]
Therefore, for a selling price of $40,000 the rancher will make the required amount of money.
A col front hit Hartford, Connecticut. The temperature dropped by 6 degrees every hour from 4:00 to 9:00 AM. If at 4:00 AM it was 9 degrees, what was the temperature at 9:00 AM?
Answer:
-21 degrees
Step-by-step explanation:
Dropping 6 degrees per hour, the temperature drops 5×6 = 30 degrees in 5 hours. Starting at 9 degrees and dropping 30, the temperature becomes -21 degrees at 9 am.
Accupril is meant to control hypertension. In clinical trials of Accupril, 2142 subjects were divided into two groups. The 1563 subjects in the experimental group received Accupril. The 579 subjects in the control group received a placebo. Of the 1563 in the experimental group, 61 experienced dizziness as a side effect. Of the 579 subjects in the control group, 15 experienced dizziness as a side effect.
Let p_1 be the true proportion of people who experience dizziness while taking Accupril. Let p_2 be the true proportion of people who experience dizziness but do not take Accupril. Create a 95% confidence interval for p_1 - p_2.
a. (0.006, 0.092)
b. (-0.06, 0.92)
c. (-0.003, 0.029)
d. (-0.04, 0.29)
Answer:
Option C.
Step-by-step explanation:
Given information
[tex]n_1=1563[/tex] and [tex]n_2=579[/tex]
[tex]x_1=61[/tex] and [tex]x_2=15[/tex]
Using the given information we get
[tex]p_1=\dfrac{x_1}{n_1}=\dfrac{61}{1563}\approx 0.039[/tex]
[tex]p_2=\dfrac{x_2}{n_2}=\dfrac{15}{579}\approx 0.026[/tex]
The formula for confidence interval for p_1 - p_2 is
[tex]C.I.=(p_1-p_2)\pm z*\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}[/tex]
From the standard normal table the value of z* at 95% confidence interval = 1.96.
[tex]C.I.=(0.039-0.026)\pm (1.96)\sqrt{\dfrac{0.039(1-0.039)}{1563}+\dfrac{0.026(1-0.026)}{579}}[/tex]
[tex]C.I.=0.013\pm (1.96)(0.008)[/tex]
[tex]C.I.=0.013\pm 0.016[/tex]
[tex]C.I.=(0.013-0.016,0.013+0.016)[/tex]
[tex]C.I.=(-0.003,0.029)[/tex]
The 95% confidence interval for p_1 - p_2. is (-0.003,0.029).
Therefore, the correct option is C.
Final answer:
The correct 95% confidence interval for the difference in proportions of dizziness between subjects taking Accupril and those not taking it, using the sample data provided, is (0.006, 0.092).
Explanation:
To create a 95% confidence interval for the difference in proportions (p_1 - p_2), where p_1 is the proportion of people who experience dizziness while taking Accupril, and p_2 is the proportion of people experiencing dizziness but not taking Accupril, we use the following formula:
Confidence Interval = (p_hat_1 - p_hat_2) ± Z*sqrt((p_hat_1*(1 - p_hat_1)/n_1) + (p_hat_2*(1 - p_hat_2)/n_2))
Where p_hat_1 and p_hat_2 are the sample proportions, n_1 and n_2 are the sample sizes, and Z is the Z-score corresponding to a 95% confidence level (1.96 for two-tailed tests).
p_hat_1 = 61/1563p_hat_2 = 15/579n_1 = 1563n_2 = 579After calculating these proportions and plugging the values into the formula, the confidence interval is (0.006, 0.092).
Hence, the correct answer is option a. (0.006, 0.092).
A force of 7 pounds is required to hold a spring stretched 0.4 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet beyond its natural length?
Final answer:
Using Hooke's Law, the spring constant is calculated from the given force and stretch, which is then used to calculate the work done for a larger stretch. The work done in stretching the spring from its natural length to 0.7 feet is approximately 4.29 foot-pounds.
Explanation:
To solve this problem, we need to use Hooke's Law, which says that the force needed to stretch or compress a spring is directly proportional to the distance the spring is stretched or compressed from its natural length. The formula for the force on a spring is F = kx, where k is the spring constant and x is the stretch from the natural length.
First, we can find the spring constant using the information given: a force of 7 pounds to stretch the spring 0.4 feet beyond its natural length.
Calculate the spring constant k: k = F / x = 7 lb / 0.4 ft = 17.5 lb/ft.Next, we use the work done by a spring force equation: Work = (1/2)kx2. To find the work done in stretching from 0 to 0.7 feet, substitute x with 0.7 in the equation.Compute the work done: Work = (1/2)(17.5 lb/ft)(0.7 ft)2 = 4.2875 foot-pounds.Therefore, the work done in stretching the spring from its natural length to 0.7 feet is approximately 4.29 foot-pounds.
he brain volumes (cm cubedcm3) of 20 brains have a mean of 1103.81103.8 cm cubedcm3 and a standard deviation of 121.9121.9 cm cubedcm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1367.61367.6 cm cubedcm3 be significantly high?
Answer: We can say that brain volume of 1367.6 cubic cm would be significantly high.
Step-by-step explanation:
Since we have given that
n = 20 brains
Mean = 1103.8 cubic. cm
Standard deviation = 121.9 cubic. cm
According to range rule of thumb, the usual values must lie within 2 standard values from the mean.
So, it becomes,
[tex]\bar{x}-2\sigma\\\\=1103.8-2\times 121.9\\\\=1103.8-243.8\\\\=860[/tex]
and
[tex]\bar{x}+2\sigma\\\\=1103.8+2\times 121.9\\\\=1103.8+243.8\\\\=1225.7[/tex]
We can see that 1376.6 does not lie within (860,1225.7).
So, we can say that brain volume of 1367.6 cubic cm would be significantly high.
Tristan and Ronna are collecting clothes for a clothing drive. Ronna collected 3 times as many clothes as Tristan did. If Tristan collected 4 1/4 bags of clothes, how many bags of clothes did Ronna collect?
Ronna collected [tex]12\frac{3}{4}[/tex] bags of clothes
Step-by-step explanation:
Tristan and Ronna are collecting clothes for a clothing drive
Ronna collected 3 times as many clothes as TristanTristan collected [tex]4\frac{1}{4}[/tex] bagsWe need to find how many bags of clothes Ronna collected
∵ Ronna collected 3 times as many clothes as Tristan did
- That means Ronna collected 3 × the amount that Tristan did
∵ Tristan collected [tex]4\frac{1}{4}[/tex] bags
- Multiply the amount of Tristan by 3 to find the amount of Ronna
∴ Ronna collected = 3 × [tex]4\frac{1}{4}[/tex]
Change the mixed number to improper fraction
∵ [tex]4\frac{1}{4}[/tex] = [tex]\frac{(4*4)+1}{4}=\frac{17}{4}[/tex]
∴ Ronna collected = 3 × [tex]\frac{17}{4}[/tex]
∴ Ronna collected = [tex]\frac{51}{4}[/tex]
Change the improper fraction to mixed number by divide 51 by 4
∵ 51 ÷ 4 = 12 and reminder 3 (4 × 12 = 48 and 51 - 48 = 3)
∴ [tex]\frac{51}{3}=12\frac{3}{4}[/tex]
∴ Ronna collected = [tex]12\frac{3}{4}[/tex] bags of clothes
Ronna collected [tex]12\frac{3}{4}[/tex] bags of clothes
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The area of one field is 16 acres and the area of the second field is 1 1/4 times bigger. A barn of wheat on the first field makes up 37 1/2 thousands of pounds per acre, and on the second 1 2/15 times as much per acre. How much more wheat was gathered from the second field than from the first?
Answer:16/15^2
Step-by-step explanation:
Answer: 250000 pounds
Step-by-step explanation:
The area of one field is 16 acres and the area of the second field is 1 1/4 times bigger. This means that the area of the second field is
1.25 × 16 = 20 acres.
A barn of wheat on the first field makes up 37 1/2 thousands of pounds per acre. This means that the total wheat on the first field will be the amount of wheat per acre × total number of acres. It becomes
37.5 × 16 = 600 000 pounds of wheat.
On the second, it is 1 2/15 times as much per acre. This means that an acre on the second field contains
17/15( converted 1 2/15 to improper fraction) times the number of wheat per acre on the first field.
Amount of wheat per acre for the second field = 17/15 × 37.5 = 42.5
This means that the total wheat on the second field will be the amount of wheat per acre × total number of acres. It becomes
42.5 × 20 = 850 000 pounds of wheat.
We will subtract the amount of wheat gathered from field 1 from the amount gathered from field 2. It becomes 850000 - 600000 = 250000 pounds of wheat. Therefore,
The amount of wheat gathered from the second field is 250000 pounds more than the amount from the first field
A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1065 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.62 hours with a standard deviation of:_____
Answer:
standard deviation is 0.51
Step-by-step explanation:
A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1065 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.62 hours with a standard deviation of 0.51
Melissa is purchasing a $160,000 home and her bank is offering her a 30-year mortgage at a 4.9% interest rate. In order to lower her monthly payment, Melissa will make a 20% down payment and will purchase 3 points. What will her monthly mortgage payment be?
Answer:650.46
Step-by-step explanation:
To calculate Melissa's monthly mortgage payment, we multiply the loan amount by the monthly interest rate, divide it by (1 - (1 + monthly interest rate) raised to the power of negative loan term in months), and finally substitute the values to get the monthly payment.
Explanation:To calculate Melissa's monthly mortgage payment, we need to consider the loan amount, interest rate, and loan term. Since she is making a 20% down payment on a $160,000 home, her loan amount will be 80% of $160,000, which is $128,000. Next, we need to calculate the monthly interest rate by dividing the annual interest rate by 12. For a 4.9% annual interest rate, the monthly interest rate is 0.049 divided by 12. Finally, we can use the formula for calculating the monthly payment on a mortgage:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Loan Term in Months))
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A team of seven workers started a job, which can be done in 11 days. On the morning of the fourth day, several people left the team. The rest of team finished the job in 14 days. How many people left the team? Show your work in an equation
Number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 days
Solution:Given that
A team of seven workers started a job, which can be done in 11 days.
On the morning of the fourth day, several people left the team. The rest of team finished the job in 14 days.
Need to determine how many people left the team.
Let say complete work be represented by variable W.
=> work done by 7 workers in 11 days = W
[tex]\Rightarrow \text {work done by } 1 \text { worker in } 11 \text { days }=\frac{\mathrm{W}}{7}[/tex]
[tex]\Rightarrow \text {work done by } 1 \text { worker in } 1 \text { day }=\frac{W}{7} \div 11=\frac{W}{77}[/tex]
As its given that for three days all the seven workers worked.
Work done by 7 worker in 3 day is given as:
[tex]=7 \times 3 \times \text { work done by } 1 \text { worker in } 1 \text { day }[/tex]
[tex]=7 \times 3 \times \frac{W}{77}=\frac{3W}{11}[/tex]
Work remaining after 3 days = Complete Work - Work done by 7 worker in 3 day
[tex]=W-\frac{3 W}{11}=\frac{8 W}{11}[/tex]
It is also given that on fourth day some workers are left.
Let workers left on fourth day = x
So Remaining workers = 7 – x
And these 7 – x workers completed remaining work in 14 days
[tex]\begin{array}{l}{\text { As work done by } 1 \text { worker in } 1 \text { day }=\frac{W}{77}} \\\\ {\text { So work done by } 1 \text { worker in } 14 \text { days }=\frac{W}{77} \times 14=\frac{2 \mathrm{W}}{11}} \\\\ {\text { So work done by } 7-x \text { worker in } 14 \text { days }=\frac{2 \mathrm{W}}{11}(7-x)}\end{array}[/tex]
As Work remaining after 3 days = [tex]\frac{8W}{11}[/tex] and this is the same work done by 7- x worker in 14 days
[tex]\begin{array}{l}{\Rightarrow \frac{\mathrm{8W}}{11}=\frac{2 \mathrm{W}}{11}(7-x)} \\\\ {=>4=7-x} \\\\ {=>x=7-4=3}\end{array}[/tex]
Workers left on fourth day = x = 3
Hence number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 days.
equation:
4=7-x
answer:
3 people left the team.
What is an Azimuth?
A. A horizontal angle measured clockwise from a north base line
B. A graphical representation of a portion of the earth’s surface
C. A graphical representation using non-magnetic means alone for measuring movement directions along the earth’s surface
D. A horizontal angle measured counterclockwise from a north base line
Final answer:
An azimuth is a horizontal angle measured clockwise from a north base line, used in navigation and surveying to indicate direction. It measures angles from 0° to 360°, starting from the north and moving towards the east, which allows for precise direction determination on the earth's surface. The correct answer is A.
Explanation:
The question, "What is an Azimuth?" pertains to how angles, specifically bearings, are measured in relation to the earth's surface. The correct answer is: 'A. A horizontal angle measured clockwise from a north base line.' An azimuth is essentially a type of bearing used in navigation and surveying to indicate direction. It is a measure of rotation from the north direction towards the east, meaning the angle increases in a clockwise fashion. The concept originates from surveying practices and is crucial for determining directions accurately on the earth's surface.
The use of azimuth in surveying involves specifying angles in degrees from 0° to 360°, starting from north towards east, south, west, and back to north. This precise measurement allows geographers, surveyors, and navigators to determine directions and locations with respect to the north base line, which serves as a universal reference point.
Furthermore, azimuth measurements can distinguish between true north, which is the geographical north pole, and magnetic north, which is dictated by the earth's magnetic field. Despite this distinction, azimuths provide a consistent method for defining bearings across various contexts, making them indispensable in mapping and navigation.
A grain silo has a cylindrical shape. Its radius is 9 ft, and its height is 53 ft. What is the volume of the silo?
Use the value 3.14 forn, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
13487 ft³
Step-by-step explanation:
Volume of a Cylinder: 2πr²*h
π = 3.14
r = 9 ft
h = 53 ft
Volume = 2(3.14)(9)²*53 = 13486.86 ft³
Rounded to nearest whole number
Volume of the Cylindrical Water tank is 13487 ft³
The volume of the cylindrical grain silo is found using the formula V = πr²h, where r is the radius and h is the height. Using the specifications of the silo (r=9 feet, h=53 feet), we find that the volume of the grain silo is about 13480 cubic feet.
Explanation:The student is trying to find the volume of a cylinder. The volume V of a cylinder can be found using the formula: V = πr²h where r is the radius of the base, h is the height and π is about 3.14.
To find the volume V of the grain silo, first, square the radius r, which is 9 feet: 81 square feet. Then multiply the result by the height h, which is 53 feet: 4293 cubic feet. Lastly, multiply the result by π, which we should approximate as 3.14: 13480 cubic feet rounded to the nearest whole number.
So, the volume of the grain silo is about 13480 cubic feet.
Learn more about Volume of Cylinderhttps://brainly.com/question/23935577
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A nonprofit organization plans to hold a raffle to raise funds for its operations. A total of 1,000 raffle tickets will be sold for $1.00 each. After all the tickets are sold, one ticket will be selected at random and its owner will receive $50.00. The expected value for the net gain for each ticket is -$0.95. What is the meaning of the expected value in this context?
Answer:
ticket owner loses an average of $0.95 per raffle ticket
Step-by-step explanation:
No profit organization plans to hold a raffle to raise funds for its operation .The expected value in this context is that ticket owner loses an average of $ 0.95
Answer:
B: The ticket owners lose an average of $0.95 per raffle ticket.
Step-by-step explanation:
Simplify x^2+3x+2/x+1
A. X+2
B. X-2
C. X^2+1
D. X^2-1
Plz explain your answer.
Answer:
[tex]\overline{BD}\ and\ \overline{AC}[/tex] bisect each other is sufficient to Prove Δ ABE ≅ Δ CDE
Step-by-step explanation:
Given: (if it is given)
[tex]\overline{BD}\ and\ \overline{AC}[/tex] bisect each other, i.e
AE ≅ CE
BE ≅ DE
To Prove:
Δ ABE ≅ Δ CDE
Proof:
In Δ ABE and Δ CDE
AE ≅ CE …………..{ BD and AC bisect each other at E}
∠ AEB ≅ ∠ CED ………….{Vertically opposite angles are equal}
BE ≅ DE ……….{ BD and AC bisect each other at E}
Δ ABC ≅ Δ PQR ….{Side-Angle-Side test} ......PROVED
Chen is keeping track of mileage to find out how many miles per gallon he gets in his truck. If he puts in 12 gallons of gas and has driven 212.4 miles since his last fill-up, how many miles per gallon does his truck get, to the nearest tenth?
Answer: 17.7
Step-by-step explanation:
212.4÷12 = 17.7
Answer: 17.7 miles per gallon
Step-by-step explanation:
Hi, to answer this question we have to divide the number of miles (212.4) by the number of gallons used (12).
Mathematically speaking:
212.4 /12 = 17.7 miles per gallon
17.7 is already rounded to the nearest tenth.
His truck gets 17.7 miles per gallon
Feel free to ask for more if needed or if you did not understand something.
PLease help!! Describe the roots of the polynomial function shown below:
Answer:
x = 1 and x = -3
Step-by-step explanation:
roots are points that y = 0
in two points we have this
x = 1 and x = -3