Find the x-intercepts of the function graphed below, and the average rate of change over the interval (-1,4).

x-intercepts:____

Average rate of change:____​

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

Answer:

$48

Step-by-step explanation:

$30+$12=$42

$90-$42=$48

Answer: she spent $48 on the jacket

Step-by-step explanation:

Lucy goes to a department store and spends $90 on clothing. This means that all the money she spent at the store is $90

She buys a dress for $30,a hat for $12, and also buys a jacket.

Let $x = the cost of the jacket. Therefore, total amount spent at the store = amount spent on dress + amount spent on hat + amount spent on jacket. It means that

90 = 12 + 30 + x

x = 90 - 12 -30 = $48

Answer: There are 60060 ways to do so.

Step-by-step explanation:

Since we have given that

Number of linden trees = 6

Number of white birch trees = 4

Number of bald cypress trees = 3

Total number of trees = 6 +4 +3 =13

So, Number of ways that the landscaper plant that trees are evenly spaced is given by

[tex]\dfrac{13\!}{6!\times 4!\times 3!}\\\\=60060[/tex]

Hence, there are 60060 ways to do so.

[tex]

\sqrt{9}=3\notin\mathbb{I} \\

\sqrt{12}=2\sqrt{3}\in\mathbb{I} \\

\sqrt{16}=4\notin\mathbb{I} \\

\sqrt{20}=2\sqrt{5}\in\mathbb{I} \\

\sqrt{25}=5\notin\mathbb{I}

[/tex]

Hope this helps.

Of the numbers shown, only √12 and √20 are irrational.

Here's why:

* Rational numbers: A rational number can be expressed as a fraction `p/q`, where `p` and `q` are integers and `q ≠ 0`.

* Irrational numbers: An irrational number cannot be expressed as a fraction `p/q`. It has a decimal representation that continues infinitely without repeating.

* √9 = 3: 3 is a rational number because it can be expressed as the fraction 3/1.

* √12: The square root of 12 cannot be simplified as a fraction. Its decimal representation is non-repeating and infinite (approximately 3.464), making it irrational.

* √16 = 4: 4 is a rational number because it can be expressed as the fraction 4/1.

* √20: The square root of 20 cannot be simplified as a fraction. Its decimal representation is non-repeating and infinite (approximately 4.472), making it irrational.

* √25 = 5:  5 is a rational number because it can be expressed as the fraction 5/1.

Therefore, the only irrational numbers in the image are √12 and √20.

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. ~0.442, b. ~0.221, c. 0, d. ~0.221. Calculated using combinations: [tex]\( \frac{C(n, k)}{C(12, 5)} \)[/tex].

To solve this problem, we can use the concept of combinations, which is a way to calculate the number of possible outcomes when order doesn't matter.

Let's define:

- [tex]\( n \)[/tex] as the total number of finalists (12 in this case)

- [tex]\( k \)[/tex] as the number of positions to be filled (5 in this case)

- [tex]\( n_F \)[/tex] as the number of female finalists (7 in this case)

- [tex]\( n_M \)[/tex] as the number of male finalists (5 in this case)

We'll use the formula for combinations:

[tex]\[ C(n, k) = \frac{n!}{k!(n - k)!} \][/tex]

where [tex]\( n! \)[/tex] represents the factorial of [tex]\( n \)[/tex], which is the product of all positive integers up to [tex]\( n \)[/tex].

a. Probability of selecting 3 females and 2 males:

[tex]\[ P(3 \text{ females, } 2 \text{ males}) = \frac{C(7, 3) \times C(5, 2)}{C(12, 5)} \][/tex]

[tex]\[ = \frac{\frac{7!}{3!4!} \times \frac{5!}{2!3!}}{\frac{12!}{5!7!}} \][/tex]

[tex]\[ = \frac{\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{5 \times 4}{2 \times 1}}{\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}} \][/tex]

[tex]\[ = \frac{35 \times 10}{792} \][/tex]

[tex]\[ = \frac{350}{792} \][/tex]

[tex]\[ \approx 0.442\][/tex]

b. Probability of selecting 4 females and 1 male:

[tex]\[ P(4 \text{ females, } 1 \text{ male}) = \frac{C(7, 4) \times C(5, 1)}{C(12, 5)} \][/tex]

[tex]\[ = \frac{\frac{7!}{4!3!} \times \frac{5!}{1!4!}}{\frac{12!}{5!7!}} \][/tex]

[tex]\[ = \frac{\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{5}{1}}{\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}} \][/tex]

[tex]\[ = \frac{35 \times 5}{792} \][/tex]

[tex]\[ = \frac{175}{792} \][/tex]

[tex]\[ \approx 0.221\][/tex]

c. Probability of selecting 5 females:

Since there are only 7 female finalists, it's impossible to select 5 females out of them for 5 positions. So, the probability is 0.

d. Probability of at least 4 females:

This includes the cases of selecting 4 females and 5 females.

[tex]$\begin{aligned} & P(\text { at least } 4 \text { females })=P(4 \text { females, } 1 \text { male })+P(5 \text { females }) \\ & =\frac{175}{792}+0 \\ & =\frac{175}{792} \\ & \approx 0.221\end{aligned}$[/tex]

So, the probabilities are:

a. Approximately 0.442

b. Approximately 0.221

c. 0

d. Approximately 0.221

Ans6:7

wer:

Step-by-step explanation:

Greatest Common Factornof 60 and 70 is 10.

60÷10 / 70÷10 =6/7

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.

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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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.

Answer:

An inscribed shape is drawn inside of another shape . A circumscribed shape is the shape drawn on the outside or around another shape .

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.

Answer:

The demand value of time lead is

a) 40

Step-by-step explanation:

X  Y Z company Uses "Continuous Review System for an item

Currently demand = 100 units

standard deviation =  20 units

lead time increase = 4 weeks

Apply Z statistic we get the value of standard deviation.

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

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.

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

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

Answer:

y=1.25x+4

Step-by-step explanation:

Number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 days

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.

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.

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

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.

Answer:

C

Step-by-step explanation:

The true statement is that proves the congruence of both triangles is:

From the complete question, we have the following highlights

The 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)

Read more about congruent triangles at:

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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

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.

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.

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.

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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).

After 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).

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

We 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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Answer:

It is 44

Step-by-step explanation:

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.

Therefore, the work done in stretching the spring from its natural length to 0.7 feet is approximately 4.29 foot-pounds.