Answer: correct answer is triangle HAE
Step-by-step explanation:
There are only chickens and pigs in Henry's Barn Henry counted a total of Sixteen animal heads and a total of 50 animal feet.How many pigs does Henry have?
Answer:
9 pigs
Step-by-step explanation:
We have the following numbers of heads:
pigs (p) + chickens (c) = 16 animal heads (1)
And the following numbers of feet:
4p + 2c = 50 animal feet (2)
From equation (1):
p = 16 - c (3)
By entering equation (3) into (2) we have:
4(16 - c) + 2c = 50
64 - 4c + 2c = 50
c = 7
Now, entering the value of c into equation (3) we have the next value of p:
p = 16 - c
p = 16 - 7
p = 9
Therefore, the number of pigs that Henry has is 9.
I hope it helps you!
Finish the work to solve the equation and find the value for p. 2.5(–3p – 8) + 5p = 4(2.25p + 5.5) + 15.5 1.Use the distributive property: –7.5p – 20 + 5p = 9p + 22 + 15.5 2.Combine like terms on each side: –2.5p – 20 = 9p + 37.5 Use the properties of equality to finish solving the equation. What is the value for p? p =
Answer:
-5
Step-by-step explanation:
Answer:
-5
Step-by-step explanation:
wHy aM i hErE?!?!
Find the missing value in the ratio table
Answer: y-value=36
Step-by-step explanation:
If you take the unit rate of these set of numbers, (it can be any set of the numbers on the table), let's use 2 and 12. To find the unit rate all you have to do is divide. 12 divided by 2 is 6. This also works for 4 and 24. 24 divided by 4 is 6. Therefore 6 times any number in the x column will give you the y-value.
Plugging in the unit rate would look look this 6(6)=y
36=y
Therefore your missing value, or the y-value that is not filled in would be 36.
Chandni has 3 pieces of orange yarn that are 1.25 feet long each and 2 pieces of blue yarn that are 2.75 feet long each. She uses all 5 pieces of yarn for an art project. What is the total length of yarn, in feet, that Chandni uses for her art project
Answer:
9.25 feet.
Step-by-step explanation:
Given:
Chandni has 3 pieces of orange yarn that are 1.25 feet long each and 2 pieces of blue yarn that are 2.75 feet long each.
She uses all 5 pieces of yarn for an art project.
Question asked:
What is the total length of yarn, in feet, that Chandni uses for her art project ?
Solution:
By unitary method:
Length of 1 piece orange yarn = 1.25 feet
Length of 3 pieces orange yarn = 1.25 feet [tex]\times[/tex] 3 = 3.75 feet
Length of 1 piece blue yarn = 2.75 feet
Length of 2 piece blue yarn = 2.75 feet [tex]\times[/tex] 2 = 5.5 feet
As she uses all 5 pieces of yarn for an art project:-
Total length of yarn, she uses for her art project = 3.75 feet + 5.5 feet = 9.25 feet
Thus, the total length of yarn, she uses for her art project = 9.25 feet.
In your job at the container factory, you are asked to design a rectangular box with volume 500 cm3 . The material for the sides and bottom costs $0.05 per cm2 while the material for the top costs $0.15 per cm2 . What dimensions do you recommend to minimize the total material cost
Answer:
6.3 cm by 6.3 cm by 12.6cm
Step-by-step explanation:
Volume of the box=[tex]500 cm^3[/tex]
The minimal dimensions of a box always occur when the base is a square.
[tex]L^2H=[/tex][tex]500 cm^3[/tex]
[tex]H=\frac{500}{L^2}[/tex]
Surface Area of a cylinder=[tex]2(L^2+LH+LH)[/tex]
Surface Area of the sides and bottom= [tex]L^2+2(LH+LH)[/tex]
Surface Area for the top = [tex]L^2[/tex]
The material for the sides and bottom costs $0.05 per [tex]cm^2[/tex]
The material for the top costs $0.15 per [tex]cm^2[/tex]
Therefore Cost of the box
[tex]C=0.15L^2+0.05[L^2+4LH]\\C=0.2L^2+0.2LH[/tex]
Recall:[tex]H=\frac{500}{L^2}[/tex]
[tex]C=0.2L^2+0.2L(\frac{500}{L^2})\\=0.2L^2+\frac{100}{L}\\C=\frac{0.2L^3+100}{L}[/tex]
The minimum value of C is at the point where the derivative is zero.
[tex]C^{'}=\frac{2(L^3-250)}{5L^2}\\\frac{2(L^3-250)}{5L^2}=0\\2(L^3-250)=0\\L^3=250\\L=6.3cm[/tex]
[tex]H=\frac{500}{L^2}=\frac{500}{6.3^2}=12.6cm[/tex]
The dimensions that would minimize the cost are 6.3 cm by 6.3 cm by 12.6cm
For each day that Sasha travels to work, the probability that she will experience a delay due to traffic is 0.2. Each day can be considered independent of the other days. What is the probability that Sasha's first delay due to traffic will occur after the fifth day of travel to work?
The probability that Sasha's first delay due to traffic will occur after the fifth day of travel to work is approximately 0.67232 or 67.232%.
The probability that Sasha will not experience a delay on any given day is 1 − 0.2 = 0.8, as the complement of the probability of experiencing a delay is the probability of not experiencing a delay.
Since each day is independent, the probability that Sasha will not experience a delay on the first day, second day, third day, fourth day, and fifth day is given by multiplying the probabilities for each day:
P(no delay on day 1 to day 5) = 0.8×0.8×0.8×0.8×0.8
Now, since we are looking for the probability that Sasha's first delay occurs after the fifth day, it means she did not experience a delay on the first five days. Therefore, the probability of the first delay occurring after the fifth day is the complement of the probability mentioned above:
P(first delay after the fifth day) = [tex]1 - 0.8^5[/tex]
Now, you can calculate this value:
P(first delay after the fifth day) = [tex]1 - 0.8^5[/tex]
P(first delay after the fifth day) = 1 − 0.32768
P(first delay after the fifth day) ≈ 0.67232
Solve using the quadratic formula x^2+4x-40=-8
The solution to the Quadratic equation [tex]x^2+4x-40=-8[/tex] is -8 & 4. correct option is C.
To solve the quadratic equation x^2+4x-40=-8 using the quadratic formula, we first need to rearrange the equation so that it is in the form [tex]ax^2+bx+c=0.[/tex]
So, the equation becomes [tex]x^2+4x-32=0.[/tex]
Now, we can identify the values of a, b, and c.
In this case, a=1, b=4, and c=-32.
Next, we can substitute these values into the quadratic formula: x = (-b±√([tex]b^2-4ac[/tex]))/(2a).
Using the formula, we can calculate the solutions for x.
After performing the calculations, we find that the solutions are x = -8 and x = 4.
Therefore, the correct answer is option c) -8 & 4.
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Jeremy is packaging a stew containers.There are 8 3/4 cups of stew that need to put into 5 to go containers equally.How many cups of stew will be in each container?
Answer:
1 3/4 cups
Step-by-step explanation:
In order to be able to equally divide the stew into 5 containers we need to turn everything into the same format, in this case it would be by multiplying the whole number and the denominator and then adding the numerator like so
(8 * 4) + 3 = [tex]\frac{35}{4}[/tex]
Now we can divide the numerator by 5 (container) in order to calculate how much stew each container will get.
[tex]\frac{35}{4} / 5 = \frac{7}{4}[/tex]
So each container will get 7/4 of the Stew or 1 3/4 cups
Answer:
Each container = 1 3/4 cups
Step-by-step explanation:
*** There are 8 3/4 cups of stew that MUST be put into five containers EQUALLY.
*** We are basically required to calculate the number of cups of stew that must be in each container.
Since 8 3/4 cups of stew needs to be equally distributed and placed in just about five containers, we will need to first convert 8 3/4 cups which is in mixed fraction into improper fraction in order to enable us to calculate successfully.
8 3/4 = [(4×8)+3]/4
= 35/4
We will now use a little bit of the principle of proportion to get through this:
If 8 3/4 cups must be equal in five containers, then one container will have ? number of cups:-
5 containers --------- 35/4 cups
1 container ---------- ? cups.
1/5 × 35/4
= 7/4 cups.
We will now convert it back to mixed fractions and we will have 1 3/4 cups.
Therefore, each container we will contain 1 3/4 cups
Nancy spent half of her allowance going to the movies. She washed the family
car and earned 7 dollars. What is her weekly allowance if she ended with
16 dollars ?
At a school play, there is a spotlight Above the center of the floor that covers a lightend area with a radius of 7 feet. What is the area covered by the spotlight
Answer:
The are of the spotlight is 14.4m
Step-by-step explanation:
Step one :
To find the area of the spotlight
First let us understand that the shape is a circle since it's a spotlight
Hence we will use the formula for area of a circle which is
A=πr²
Step two :
Given r= 7feet - - - >metre =2.14m
i.e
1foot =0.305m
7feet =xm
Crosss multiplying we have
X=7*0.305=2.14m
π= 3.142
Step three :
Substituting into the formula we have
A=3.412*2.14²
A=3.142*4.58
A=14.4m
Answer:
154 square feet
Step-by-step explanation:
Extracting the key information from the question:-
*** At school play, there's spotlight above centre of floor.
*** This covers a light end area with radius 7 feet.
*** We are required to calculate the area covered by the spotlight.
In other words, we are basically required to calculate the area of a circle because it is almost certain that the area it covers will be a perfect circle. So all we need to do is to put down the formula for calculating the area of a circle.
We already know that the radius here is 7 feet. We will now simply draft this into the formula and we are good to go.
Formula for area of a circle = πr^2. π = 22/7, r = radius = 7 feet.
Then 22/7 × 7 × 7
= 154 feet^2. The area that is covered by the spotlight which is a perfect circle = 154ft^2
Find the length of RS.
Given:
The length of arc TS = 40 in
To find:
The length of arc RS.
Solution:
Length of TS = 40 in
θ = 80°
Using arc length formula:
[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]
[tex]$40=2 \times 3.14 \times {r}\left(\frac{80}{360}\right)[/tex]
[tex]$40=6.28 \times {r}\left(\frac{2}{9}\right)[/tex]
[tex]$40=1.39\times r[/tex]
Divide by 1.39 on both sides, we get
[tex]28.7=r[/tex]
Radius = 28.7
Complete angle of circle = 360°
Angle measure of RS = 360° - 60° - 120° - 80°
Angle measure of RS = 100°
Arc length of RS:
[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]
Substitute θ = 100° and r = 28.7
[tex]$=2 \times 3.14 \times 28.7 \left(\frac{100}{360}\right)[/tex]
= 50 inch
The length of arc Rs is 50 inches.
A newborn who weighs 2,500 g or less has a low birth weight. Use the information on the right to find the z-score of a 2,500 g baby. In the United notes, birth weights of newborn babies are approximately normally distributed with a mean of mu = 3,600 grams and a standard deviation of sigma = 500 grams. Z = StartFraction x minus mu Over sigma EndFraction
Answer:
[tex]Z = -2.2[/tex]
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 3600, \sigma = 500[/tex]
Use the information on the right to find the z-score of a 2,500 g baby.
This is Z when X = 2500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2500 - 3600}{500}[/tex]
[tex]Z = -2.2[/tex]
Answer:
Step-by-step explanation:
-2
ur welcome ;)
find the angle in standard position whose cosine is 1/2
A 5π/3
B π/3
C π/3 and 5π/3
D 4π/3 and 2π/3
Answer:
C is the correct answer
Step-by-step explanation:
In this question, we are tasked with calculating the angle at standard position which has a cosine value of 1/2
With reference to the cartesian coordinates, there are only two quadrants which has positive valued for Cosine. These are the first quadrant and the last or 4th quadrant. While the first quadrant has angles in the range of 0-90 the fourth quadrant has an angle range from 270-360
Now back to the angle. In the first quadrant, the angle that has cosine value equal to 30 is cos 60. This is same as pi/3 radians
Now the general form of the angle on the fourth quadrant is 360-theta
Thus, since our theta is pi/3, which is 60, that angle on the fourth quadrant having same value as 1/2 is 360-60 = 300
This is same as 5pi/3 radians
So our answers are pi/3 radians and 5pi/3 radians where pi radians is same as 180 degrees
Please I need help with the following question, How can you obtain the graph of ( + )from the graph of ?
Answer:
B) Translate the graph [tex] k [/tex] units to the left.
You roll a 6-sided die. What is the probability of rolling a 4? Write it as a fraction. P(4)=
Answer:
P(4)= 1/6
Step-by-step explanation:
Lots of Love!! <3
Stay Safe! Stay at Home!! =)
Answer:
Step-by-step explanation:
no of sample space, n(s) = 6
no of favorable cases , n(e) = 1
Probability of getting 4,
P(e) = n(e) / n(s)
= 1 / 6
LOTS OF POINTS IM DESPERATE! can someone please refresh my memory on a couple of log equations? Thank you!
Answer:
78. t=8.66yrs
79. r=23.10%
80. r=11.0975%
Step-by-step explanation:
78. Given the initial deposit is $1,000 and the 8% compounded continuously. The doubling time can be calculated using the formula;
[tex]A=Pe^{it}[/tex]
Given that A=2P, we substitute in the equation to solve for t:
[tex]A=Pe^{rt}\\\\2P=Pe^{rt}\\\\2=e^{0.08t}\\\\0.08t=\ In 2\\\\t=8.66\ years[/tex]
Hence, it takes 8.66 years for $1,000 to double in value.
79.
Given the initial deposit is $1,000 and the r% compounded continuously.
-The doubling rate can be calculated using the formula;
[tex]A=Pe^{rt}[/tex]
#We substitute our values in the equation to solve for r:
[tex]A=Pe^{rt}\\\\A=2P, t=3\\\\\therefore\\\\2P=Pe^{3r}\\\\2=e^{3r}\\\\r=\frac{In \ 2}{3}\\\\=0.23105\approx 23.10\%[/tex]
Hence, the deposit will double in 3 years at a rate of 23.10%
80.
Given the initial deposit is $30,000 and the future value is $2,540,689.
-Also, given t=40yrs, the rate of growth for continuous compounding is calculated as:
[tex]A=Pe^{rt}, \ \ \ r=r, t=40yrs\\\\2540689=30000e^{40r}\\\\\frac{2540689}{30000}=e^{40r}\\\\r=\frac{In \ (2540689/30000)}{40}\\\\\\=0.110975=11.0975\%[/tex]
Hence, the deposit will grow at a rate of approximately 11.0975%
Marvin earns $7.25 per hour at his summer job. He wants to buy a video game system that costs $166.75. Enter an equation to model the relationship between the number of hours worked h and the amount earned e
Answer:
7.25h = e
If e = $166.75, h = 23 hours
Step-by-step explanation:
7.25h = e
However many hours he works, he'll earn 7.25 times that number.
If he wants to know how many hours he must work to get the video game system where e = 166.75, we model this with
7.25h = e
7.25h = 166.75
Divide both sides by 7.25.
h = 23 hours
Final answer:
Explanation of the equation relating hours worked to earnings and interpretation of variables.
Explanation:
Equation: e = 7.25h - 166.75
Explanation: The equation that models the relationship between the number of hours worked h and the amount earned e can be represented as e = 7.25h - 166.75. This equation captures the idea that Marvin earns $7.25 per hour and wants to buy a video game system costing $166.75.
Independent and dependent variables: Hours worked (h) is the independent variable, and the amount earned (e) is the dependent variable. The y-intercept is -166.75, and the slope is 7.25, indicating that for each additional hour worked, Marvin earns $7.25.
A random sample of people was asked to report the age and distance driven of their primary car. A line was fit to the data to model the relationship.
Answer:
y= 12x + 5 for part A, part B is 89 thousand miles
Step-by-step explanation:
Just copy the answer you nerd.
A certain television is advertised as a 17-inch TV(the diagonal length). If the width of the TV is 8 inches, how many inches tall is the Tv?
Answer:
15
Step-by-step explanation:
-5x -4y = -15 and -x + 4y = -3
So the first thing you would want to do is rewrite the equation like so.
−x+4y=−3;−5x−4y=−15
once you done that you'll have to think about what variable are you trying to get be itself which in this case it'll be x. So now you'll be solving this equation.
−x+4y=−3
next you'll add -4y to both sides
Once you done so you should have this written down
-x over -1 = 4y- 3 over -1
divide -1 to both sides and you should end up with x= 4y+3
Now you have to substitute 4y+3 for x in -5x-4y=-15
So it should look like this now
−5(4y+3)−4y=−15
The next step is to simplify both sides with the following equation
−24y−15=−15
After simplifying add 15 to both sides, It then should look like this
−24y=0
Divide -24 to both sides and your answer should be this
y=0
hope this helps :)
What is the distance between (3,5.25 and (3,-8.75)
Answer:
Step-by-step explanation:
hello :
the distance between (3,5.25 and (3,-8.75) is :
√((3-3)²+(5.25+8.75)²) ......continu
Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. b equals 6 comma c equals 8 comma Upper B equals 30 degrees
The information given results in one triangle. By applying the law of sines and trigonometric relation, we find the angles A=107.52, B=30, C=42.48 degrees for a triangle with sides b=6, c=8.
Explanation:The problem deals with the Law of Sines which can be used to determine if a triangle exists given two sides and a non-included angle. According to the law of sines, ratio of the length of a side to the sine of the opposite angle is the same for all three sides of a triangle. Using this, we can determine whether the given conditions lead to a valid triangle.
Given: b = 6, c = 8, B = 30 degrees
1. Compute the value of sin(B) = sin(30) = 0.5 (using standard angle values).
2. Apply the law of sines to compute the missing angle. You get sin(C) = c*sin(B)/b = 8*0.5/6 = 0.67
3. Check sin(C): if sin(C) is greater than 1 or less than -1, no triangle exists. If sin(C) = 0.67, we get C = arcSin(0.67) = 42.48 degrees.
4. To find the third angle A, use the relationship 'Sum of angles in a triangle' equals 180. Hence, A = 180 - B - C = 180 - 30 - 42.48 = 107.52 degrees. We know that in a triangle, no angle can exceed 180 degrees, hence A=107.52 degrees confirms that the triangle is possible.
Hence given information results in one triangle with sides b=6, c=8 and angles A=107.52, B=30 and C=42.48
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The given information results in one triangle. To solve the triangle, we can use the Law of Sines.
Explanation:The given information of b=6, c=8, and B=30 degrees results in one triangle.
To solve the triangle, we can use the Law of Sines.
By plugging in the values, we can find the length of side a using the formula: a = (b * sin(A)) / sin(B).
After substituting the values, we find that the length of side a is approximately 3.464 units.
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There are 10 people on a basketball team, and the coach needs to choose 5 to put into a game. How many different possible ways can the coach choose a team of 5 if each person has an equal chance of being selected?
To find out how many different possible ways the coach can choose 5 players from a team of 10, we calculate the combinations using the formula C(10, 5) which results in 252 different possible ways.
Explanation:To find out how many different possible ways the coach can choose a team of 5 from 10 players, we use combinations. In mathematics, a combination is a selection of items from a larger set, where the order of selection does not matter. This is often denoted as C(n, k) or sometimes nCk, where n represents the total number of items to choose from, in this case, 10 players, and k is the number of items to choose, which here is 5 players.
The formula for a combination is:
C(n, k) = n! / (k!(n-k)!)
where ! denotes factorial, which is the product of all positive integers up to that number.
So for our specific question:
C(10, 5) = 10! / (5!(10-5)!) = 10! / (5!*5!) = (10*9*8*7*6) / (5*4*3*2*1) = 252
Therefore, there are 252 different possible ways the coach can choose a team of 5 players from a pool of 10.
Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.
Which is more expensive and by how much?
Answer:
24 is more expensive by $18.00
Step-by-step explanation:
Answer:
The eight pounds of peanuts are more expensive, by $1.
Step-by-step explanation:
If eight pounds of peanuts cost $24.00, then one pound of peanuts costs $24.00/8 = $3.00.
If six pounds of walnuts cost $12.00 (half as much), then one pound of walnuts costs $12.00/6 = $2.00.
Please help, I have to find the missing coordinate
Answer:
(14, 6)
Step-by-step explanation:
If you plug in 6 for y you get:
6 = x/2 - 1
Add 1 to both sides:
7 = x/2
Multiply 2 on both sides:
14 = x
The answer is (14, 6)
two numbers have these properties both numbers are greater than 8 their highest common factor is 8 their lowest common multiple is 40 find the two numbers
Answer:
8 and 40
Step-by-step explanation:
Both area multiples of 8:
8, 16, 24, 32, 40
40 = 8 × 5
Since 5 is prime, it can only be:
8 and 40
Why is the value of x limited to 0 in. < x < 4.25 in.?
Answer:
Lengths can't be negative
Step-by-step explanation:
Dimensions of the base are:
(8.5-2x) × (11 - 2x)
Since length cannot be negative:
x > 0
8.5 - 2x > 0
2x < 8.5
x < 4.25
11 - 2x > 0
x < 5.5
The set of values of x which satisfies all is:
0 < x < 4.24
Rachel is investing $14,000 in a CD at a bank. If the bank uses simple interest and the bank pays 2.5% annually, how much will the CD be worth in total at the end of 7 years when the CD matures?
Answer:
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount of money invested.
P represents the principal or amount of money invested.
R represents interest rate on the investment.
T represents the duration of the investment in years.
From the information given,
P = $14000
R = 2.5%
T = 7 years
Therefore,
I = (14000 × 2.5 × 7)/100
I = $2450
The total amount that the CD would be worth after 7 years is
14000 + 2450 = $16450
Answer:
Value of CD in total at the end of 7 years when the CD matures is $16646
Step-by-step explanation:
This is based on the formula A= P(1+r)^ n
where r = annual rate of interest,
P = Principal amount,
n = number of years
p = 14000
r = 2.5
n = 7
A = 14000 ( 1+ 0.025) ^ 7
= 14000 ( 1.025)^7
=14000 x 1.189
=16646
A = $16646
Find the requested value.
f(-6) for f(x) =
Select one:
A. 12
B. -12
C. 3
D. -9
Answer:
C
Step-by-step explanation:
The reciprocal of 11/7
[tex]\Huge{\underline{\underline{\tt{\orange{Answer:}}}}}[/tex]
Reciprocal of 11/7 is 7/11.Reason :
Reciprocal is also known as multiplicative inverse which means the number is to be multiplied with the given number to give the result 1.If we flip 11/7 , it becomes 7/11 , and if 7/11 is multiplied with 11/7 ,the result is 1.Usage :Reciprocal is generally used for division in which the second number is reciprocated and the division sign is converted into the multiplication sign. Then the number is simplified and we obtain our answer.__________________________________________
The reciprocal of the given fraction 11/7 is 7/11.
What is the reciprocal property?The reciprocal of any quantity is, one divided by that quantity. For any number ‘a’, the reciprocal will be 1/a. If the given number is multiplied by its reciprocal, we get the value 1.
The given fraction is 11/7.
The reciprocal of the given fraction is the fraction that results from switching or reversing the numerator and denominator.
The reciprocal of the fraction is 7/11.
Therefore, the reciprocal of the fraction is 7/11.
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