I need help please can not figure out this problem

Answer:

Our two intersection points are:

[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]

Step-by-step explanation:

We want to find where the two graphs given by the equations:

[tex]\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1[/tex]

Intersect.

When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.

Since the linear equation is easier to solve, solve it for y:

[tex]\displaystyle y = -\frac{3}{4} x + \frac{1}{4}[/tex]

Substitute this into the first equation:

[tex]\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16[/tex]

Simplify:

[tex]\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16[/tex]

Square. We can use the perfect square trinomial pattern:

[tex]\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16[/tex]

Multiply both sides by 16:

[tex](16x^2+32x+16)+(9x^2-54x+81) = 256[/tex]

Combine like terms:

[tex]25x^2+-22x+97=256[/tex]

Isolate the equation:

[tex]\displaystyle 25x^2 - 22x -159=0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 25, b = -22, and c = -159. Substitute:

[tex]\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}[/tex]

Hence, our two solutions are:

[tex]\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}[/tex]

We have our two x-coordinates.

To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:

[tex]\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2[/tex]

And:

[tex]\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}[/tex]

Thus, our two intersection points are:

[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]

These are variables on your graph

Answer:

$64.15

Step-by-step explanation:

to solve this problem, first we should figure out how much money that the cashier gave them back, and then subtract that from $80 (which was what Matt and his siblings gave the cashier) to find out how much the perfume cost.

it is given that:

they gave the cashier $80.

the cashier gave them back 1 ten-dollar bill ($10), 1 five-dollar bill ($5), 8 dimes ($0.80 or 80 cents) , and 1 nickel ($0.05 or 5 cents)

$10+$5+$0.80+$0.05=$15.85

the total amount of money that the cashier gave them back is $15.85

to find how much the perfume cost:

$80-$15.85=$64.15

so, the perfume cost $64.15

Answer:

The standard deviation for the number of defective parts in the sample is 1.88.

Step-by-step explanation:

The sample is with replacement, which means that the trials are independent, and thus, the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.  

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

68 defective out of 400:

This means that [tex]p = \frac{68}{400} = 0.17[/tex]

From the shipment you take a random sample of 25.

This means that [tex]n = 25[/tex]

Standard deviation for the number of defective parts in the sample:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{25*0.17*0.83} = 1.88[/tex]

The standard deviation for the number of defective parts in the sample is 1.88.

The standard deviation of the situation is 1.88

The proportion of success is calculated as:

[tex]p = \frac xn[/tex]

So, we have:

[tex]p = \frac {68}{68 + 332}[/tex]

[tex]p = 0.17[/tex]

The standard deviation is then calculated as:

[tex]\sigma= \sqrt{np(1-p)}[/tex]

For a shipment of a random sample of 25, we have:

[tex]\sigma= \sqrt{25 * 0.17 * (1-0.17)}[/tex]

Evaluate the product

[tex]\sigma= \sqrt{3.5275}[/tex]

Evaluate the root

[tex]\sigma= 1.88[/tex]

Hence, the standard deviation of the situation is 1.88

Read more about standard deviation at:

https://brainly.com/question/475676

Answer:

(230.21 ; 233.13)

Step-by-step explanation:

Given the data :

230.66, 233.05, 232.58, 229.48, 232.58

To calculate the 90% CI

WE obtain the mean and standard deviation of the sample data :

Mean of sample, ΣX /n = 1158.35/5 = 231.67

The standard deviation of the sample, s = 1.531 (Using calculator).

(The 90% Tcritical value, 2 sided, df = 4) = 2.132

The confidence interval, CI :

Mean ± Tcritical * s/√n

C.I = 231.67 ± (2.132 * (1.531/√5)

C. I = 231.67 ± 1.4597

(231.67 - 1.4597) ; (231.67 + 1.4597)

(230.21 ; 233.13)

Answer:

2√10

Step-by-step explanation:

Given the following data;

Area of square = 40

Mathematically, the area of a square is calculated by using the formula;

Area, A = s²

Where;

s is the length of sides of a square.

Substituting into the formula, we have;

40 = s²

s = √40

s = √4 * √10

s = 2 * √10

s = 2√10

Answer:

D. 0.42

Step-by-step explanation:

First, convert 40 km to miles by dividing it by 1.6:

40/1.6

= 25

Create a proportion where x is the number of gallons the motorcycle will need to travel 40 km (25 miles):

[tex]\frac{60}{1}[/tex] = [tex]\frac{25}{x}[/tex]

60x = 25

x = 0.4166

Round this to the nearest hundredth:

x = 0.42

So, to travel 40 km, the motorcycle will need 0.42 gallons of fuel.

The correct answer is D. 0.42

Answer:

x = 42

Step-by-step explanation:

24+8 = 32

[tex]\frac{x}{24}[/tex] = [tex]\frac{x+14}{32}[/tex]

32x = 24(x+14)

32x = 24x+336

8x = 336

x = 42

this is a special triangle so v = 17

u = 17√2

Answer:

v = 17

u = 17[tex]\sqrt{2}[/tex]

Step-by-step explanation:

If v = 17 (it is because it is a right triangle, so the pythagorean theorum works, and triangles are 180 degrees, so 180 - 90 = 90, so the other two angles are 45 degrees, meaning that v is the same length as 17.) then

17 ^ 2 = u ^2

289 = u^2

17 root to 2

9514 1404 393

Answer:

  398.2 cm²

Step-by-step explanation:

The area of the whole circle is ...

  A = πr²

  A = π(13 cm)² = 169π cm²

The 270°  sector is 3/4 of the whole circle, so its area is ...

  sector area = (3/4)(169π cm²) ≈ 398.2 cm²

Answer:

24.12

Explanation --

Circumference = Pi x D (d --> diameter)

Diameter = 2r (r --> radius)

4+4 (4[2]) = 8

3.14 times 8 (8 is the diameter we just found out, while 3.14 is pi) -->

25.12

Hope this helps!!

Answer:  c=πd

we need 'd'

hence,

d=2r

d=2(4cm)

d=8cm

now,

c=3.14×8cm

c=25.12cm

9514 1404 393

Answer:

  5

Step-by-step explanation:

A calculator can be useful when you want to evaluate a numerical expression.

__

The applicable rules of exponents are ...

  a^-b = 1/a^b

  a^0 = 1 . . . . . . a≠0

__

Your expression evaluates to ...

  (1/5)^-1 × 4^0 = (5/1)^1 × 1 = 5

Answer:

Had a problem in school like this, all you gotta dois ta

Answer:

e < 24 is the inequality which shows the possible earnings per share.

Explanation:

x, will stand for the variable for earnings and less than, means it will not be higher nor the same as 24. Thus, being leaves us with one sign. The open part facing 24 means that 24 is the bigger number, therefore the smaller side represents that x has to be smaller than 24.

Answer: x<24

Step-by-step explanation:

x, will stand for the variable for earnings and less than means it will not be higher nor the same as 24. Thus being leaves us with one sign. The open part facing 24 means that 24 is the bigger number therefore the smaller side represents that x has to be smaller than 24.

Answer:

No, they are not.

Step-by-step explanation:

If you distributed 12(x - 4y), you would get 12x - 48y. If you distributed 3(3x-y), you would get 9x- 3y. 12x - 48y and 9x - 3y are not equivalent. Hope this helped!

Answer:

C. all possible input values of the function

Step-by-step explanation:

Answer:

C is right

Step-by-step explanation:

domain is f(x)=x^2 is all real numbers but domain g(x)=1/x is all real numbers except for 0 which is x but domains and the rang can be the same also

9514 1404 393

Answer:

  x = 30

Step-by-step explanation:

In an arithmetic sequence, any given term is the average of the two terms that come before and after. The middle term of this sequence must be ...

  2sin(3x) = (-11 +15)/2

  sin(3x) = 1 . . . . . . . . . . simplify and divide by 2

Then the value of 3x must be 90°, so ...

  x = 90/3 = 30

There is one value of x in the interval [0, 90] that makes this sequence arithmetic: x = 30.

Answer:

show us a screenshot or image

or type it out, copy paste

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Slope formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

x1 = 1

y1 = 8

x2 = -3

y2 = 12

[tex]\frac{12-8}{-3-1}[/tex]

[tex]\frac{4}{-4}[/tex] = -1

Answer:

0.7734 = 77.34% probability that at least 22 will contain an error. Probability above 50%, which means that this is likely to occur.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

About 12.5% of restaurant bills are incorrect.

This means that [tex]p = 0.125[/tex]

200 bills are selected at random

This means that [tex]n = 200[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 200*0.125 = 25[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.125*0.875} = 4.677[/tex]

Find the probability that at least 22 will contain an error.

Using continuity correction, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{21.5 - 25}{4.677}[/tex]

[tex]Z = -0.75[/tex]

[tex]Z = -0.75[/tex] has a p-value of 0.2266.

1 - 0.2266 = 0.7734

0.7734 = 77.34% probability that at least 22 will contain an error. Probability above 50%, which means that this is likely to occur.

Answer:

1

Step-by-step explanation:

1 increased by 3=1+3=4

Twice of 1=1+1=2

4 is two more than 2.

Therefore, the number=1

Answer:

what is thia

Step-by-step explanation:

i have no idea what you juat said like fr what topic is this im too bored to read the queation

The input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.

Given information:

A medical researcher is using rats to do an experimental test to determine the appropriate dosage for a new cancer drug.

Each rat will be given a different dosage of the drug.

The oncologist will then measure the growth rate of the cancerous tumor.

Now, in the experiment, the oncologist tries to study or calculate the growth rate of a cancerous tumor. So, the output that he/she will get will be the growth rate of the cancerous tumor.

The experiment is done on the rate by giving them a dosage of the drug. The dosage can vary based on the study criterion. So, the amount of dosage of the drug should be the input of the experiment.

Therefore, the input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.

For more details, refer to the link:

https://brainly.com/question/5527886

Answer:

0.08y - 0.0144

Step-by-step explanation:

We need to solve the below expression i.e.

(y - .18) x .08

It can be done as follows :

Using distributive property to solve it.

(y - .18) x .08 = 0.08(y) - 0.18(0.08)

= 0.08y - 0.0144

So, the equivalent expression is 0.08y - 0.0144.

Answer:

False

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

West University:

15 out of 100, so:

[tex]p_W = \frac{15}{100} = 0.15[/tex]

[tex]s_W = \sqrt{\frac{0.15*0.85}{100}} = 0.0357[/tex]

East University:

12 out of 100, so:

[tex]p_E = \frac{12}{100} = 0.12[/tex]

[tex]s_E = \sqrt{\frac{0.12*0.88}{100}} = 0.0325[/tex]

Test the difference in driving abilities at the two universities:

At the null hypothesis we test if there is no difference, that is, the subtraction of the proportions is 0, so:

[tex]H_0: p_W - p_E = 0[/tex]

At the alternative hypothesis, we test if there is a difference, that is, if the subtraction of the proportions is different of 0. So

[tex]H_1: p_W - p_E \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = p_W - p_E = 0.15 - 0.12 = 0.03[/tex]

[tex]s = \sqrt{s_W^2+s_E^2} = \sqrt{0.0357^2+0.0325^2} = 0.0483[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.03 - 0}{0.0483}[/tex]

[tex]z = 0.62[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the proportions differ by at least 0.03, which is P(|z| > 0.62), that is, 2 multiplied by the p-value of z = -0.62.

Looking at the z-table, z = -0.62 has a p-value of 0.2676.

2*0.2676 = 0.5352.

The p-value of the test is 0.5352 > 0.05, which means that the difference in driving is not statistically significant at the .05 significance level, and thus the answer is False.

Answer:

The answer is "2"

Step-by-step explanation:

When we check the points where the x is -2

by calculating the "y-value":

It is 2, right?  

it implies that [tex]f(-2)=2[/tex]

that's why the final answer is "2"

Answer:

4/6

Step-by-step explanation:

Just a guess

Answer:

11

Step-by-step explanation:

we have as many numbers as dots

like 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 13 13 14 15 15 16 16 17 18

so in the middle it's 11 and 11

(11+11)÷2=11

9514 1404 393

Answer:

  A.  1

Step-by-step explanation:

Arc AB is twice the measure of the angle ABC. The sum of the arc measures around the circle is 360°.

  2(43x)° +(272x +2)° = 360°

  358x +2 = 360 . . . . . . . . . . . . divide by °, collect terms

  358x = 358 . . . . . . . . subtract 2

  x = 1 . . . . . . . . . . divide by 358