In a certain Algebra 2 class of 23 students, 11 of them play basketball and 13 of them play baseball. There are 8 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Answer:

[tex]5cm ^{3} [/tex]

Step-by-step explanation:

[tex]v = whl \\ = \frac{5}{2} \times \frac{4}{1} \times \frac{1}{2} \\ = \frac{20}{4} \\ = 5 {cm}^{3} [/tex]

Answer:

QS=51

Step-by-step explanation:

It was given that RS = 19 and QR =32

QS=x

Q-R was measured and found to be 32

R-S was measured and found to be 19

Q-S will be the sum of Q-R and R-S which is 32+19= 51

QS=51

Answer:

51

Step-by-step explanation:

I took the test and it was correct :)

Answer:

Base price: $13.

Surcharge: $2 per additional pound.

Step-by-step explanation:

The base price can be considered a constant, while the surcharge is a function of the additional weight of the package, over 1 pound.

Then, we can model this as a linear function, with additional weight as the independent variable.

[tex]f(x)=b+sx[/tex]

being b: base price, and s: surcharge for each additional pound.

The 7-pound package cost $25. The additional weigth in this case is 7-1=6 pounds.

The 22-pound package cost $55. The additional weigth is 21 pounds.

So we have the first point (6, 25):

[tex]f(6)=b+s(6)=25\\\\b=25-6s[/tex]

Then, for the second point (21, 55) we have:

[tex]b=25-6s\\\\f(21)=(25-6s)+s(21)=55\\\\25+(21-6)s=55\\\\15s=55-25=30\\\\s=30/15=2\\\\\\b=25-6(2)=25-12=13[/tex]

Then, the prices are:

Base price: $13.

Surcharge: $2 per additional pound.

Answer:

Step-by-step explanation:

Given the equation model 4x+(-4) = -2x+8

To find the value of x, the following steps must be followed

[tex]4x+(-4) = -2x+8\\4x-4 = -2x+8\\subtracting\ 8\ from\ both\ sides\\4x-4-8=-2x+8-8\\4x-12=-2x\\4x+2x=12\\6x=12\\x=\frac{12}{6}\\ x = 2[/tex]

The value of x is 2

Question:

The model below represents 4x + (-4) = -2x + 8.

4 long green tiles and 4 square red tiles = 2 long red tiles and 8 square green tiles.

What is the value of x when solving the equation 4x + (-4) = -2x + 8 using the algebra tiles?

x = -4

x = -2

x = 2

x = 4

Answer:

x = 2

Step-by-step explanation:

Given

4x + (-4) = -2x + 8 which represents a model of coloured tiles of various lengths (shapes)

Required

Find x

To find x, we'll solve the expression 4x + (-4) = -2x + 8 using the knowledge of algebra.

4x + (-4) = -2x + 8

Open bracket

4x - 4 = -2x + 8

Collect like terms

4x + 2x = 4 + 8

Perform addition arithmetic operation on both sides of the equation

6x = 12

Multiply both sides by ⅙

⅙ * 6x = ⅙ * 12

x = 2

Hence, the value of x that satisfies the expression 4x + (-4) = -2x + 8 is 2

Answer: 6.6

Step-by-step explanation:

We have two triangles. Find the hypothenuse of the first triangle to make it easier to solve the second triangle.

First triangle:

a = 6

b = 8

c = ?

Use pythagorean's theorem

[tex]c^2=a^2+b^2\\c=\sqrt{a^2+b^2}[/tex]

[tex]c=\sqrt{(6)^2+(8)^2}\\ c=\sqrt{36+64}\\ c=\sqrt{100}\\ c=10[/tex]

This hypothenuse is valid for both triangles. Having said this, we already have 2 sides of the second triangle; c and a. We need to find b.

[tex]c^2=a^2+b^2\\b^2=c^2-a^2\\b=\sqrt{c^2-a^2}[/tex]

[tex]b=\sqrt{(12)^2-(10)^2}\\ b=\sqrt{144-100}\\ b=\sqrt{44}\\ b=6.6[/tex]

[tex]\dfrac{y+1}{y+2}+\dfrac{y+8}{y+9}=\dfrac{y+2}{y+3}+\dfrac{y+7}{y+8}[/tex]

Write all fractions in terms of a common denominator:

[tex]\dfrac{y+1}{y+2}=\dfrac{(y+1)(y+9)(y+3)(y+8)}{(y+2)(y+9)(y+3)(y+8)}[/tex]

[tex]\dfrac{y+8}{y+9}=\dfrac{(y+8)^2(y+2)(y+3)}{(y+2)(y+9)(y+3)(y+8)}[/tex]

[tex]\dfrac{y+2}{y+3}=\dfrac{(y+2)^2(y+9)(y+8)}{(y+2)(y+9)(y+3)(y+8)}[/tex]

[tex]\dfrac{y+7}{y+8}=\dfrac{(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}[/tex]

Then move all fractions to one side and simplify the numerator:

[tex]\dfrac{(y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}=0[/tex]

The numerator dictates when the fraction reduces to 0. The denominator can never be 0, so we know that y cannot take any of the values -2, -9, -3, nor -8.

So the equation reduces to

[tex](y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)=0[/tex]

Expand the left side; you would end up with

[tex]-6(2y+11)=0[/tex]

[tex]2y+11=0[/tex]

[tex]2y=-11[/tex]

[tex]\implies\boxed{y=-\dfrac{11}2}[/tex]

Answer:

146

Step-by-step explanation:

j=3 13 = 39

g=5 13 = 65

a=4 13 = 42

Answer:

156 sweets

Step-by-step explanation:

3+4+5=12

12/12 x 39 x 12/3=156 sweets

Answer:

Step-by-step explanation:

Answer:

We conclude that the population mean light bulb life is at least 500 hours at the significance level of 0.01.

Step-by-step explanation:

We are given that a manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. The population standard deviation is 50 hours and the light bulb life is normally distributed.

You select a sample of 100 light bulbs and find mean bulb life is 490 hours.

Let [tex]\mu[/tex] = population mean light bulb life.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 500 hours      {means that the population mean light bulb life is at least 500 hours}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 500 hours     {means that the population mean light bulb life is below 500 hours}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                           T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean bulb life = 490 hours

           σ = population standard deviation = 50 hours

           n = sample of light bulbs = 100

So, the test statistics  =  [tex]\frac{490-500}{\frac{50}{\sqrt{100} } }[/tex]

                                     =  -2

The value of z test statistics is -2.

Now, at 0.01 significance level the z table gives critical value of -2.33 for left-tailed test.

Since our test statistic is higher than the critical value of z as -2 > -2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population mean light bulb life is at least 500 hours.

Answer:

option A is your answer in my opinion.

Sry i am not sure

Answer:

14000

Step-by-step explanation:

A year he contributes :10/100 × 80000= 8000

Then his employer pays 0.75 × 8000= 6000

The total money contributed to is

401k is = 8000 + 6000 = 14000

Answer:

[tex] P=12000, r= 0.04, t=3[/tex]

And n=4 since the rate is compounded quarterly, so then replacing this info we got:

[tex] A = 12000 (1+ \frac{0.04}{4})^{4*3} = 13521.9[/tex]

So then Mario will have about $13521.9 after the 3 years with the rate of interest used.

Step-by-step explanation:

For this case we can use the formula for future value based on a compound interest given by:

[tex] A= P (1+ \frac{r}{n})^{nt}[/tex]

Where A represent the future value, P the present value or the inversion r is the rate of interest on fraction, n the number of times that the rate of interest is compounded in a year and t the number of years.

For this case we know this:

[tex] P=12000, r= 0.04, t=3[/tex]

And n=4 since the rate is compounded quarterly, so then replacing this info we got:

[tex] A = 12000 (1+ \frac{0.04}{4})^{4*3} = 13521.9[/tex]

So then Mario will have about $13521.9 after the 3 years with the rate of interest used.

Answer: D. 0, pi/6, pi, 5pi/6, and 2pi

Step-by-step explanation:

Refer to screenshot of Desmos graph below

Question: What are all the exact solutions of [tex]2sin^2x-sinx=0[/tex] for [tex]0\leq x\leq 2\pi[/tex]?

Answer:

Step-by-step explanation:

If we let c and p represent the cups of cheese and plates of nachos, we have ...

  c = 2/3p . . . . . each plate of nachos requires 2/3 cups of cheese

Solving for p, we find ...

  (3/2)c = p . . . . . multiply by 3/2

Then for 5 cups of cheese, we have ...

  (3/2)(5) = p = 15/2 = 7 1/2 . . . . plates of nachos

5 cups of cheese will make 7 full plates of nachos.

__

For 9 plates of nachos, we need ...

  c = 2/3(9) = 6 . . . . . . cups of cheese

Since we have 5 cups of cheese, we need 1 more cup of cheese to make 9 plates of nachos.

Answer:

5.5

Step-by-step explanation:

5x-2.5+6x-3=_____(2x-1)

11x-5.5=5.5(2x-1)

11x-5.5=11x-5.5

Answer:

5.5

Step-by-step explanation:

Answer:

The 95% confidence interval for the overall noncompliance proportion is (0.0387, 0.1169).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 180, \pi = \frac{14}{180} = 0.0778[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0778 - 1.96\sqrt{\frac{0.0778*0.9222}{180}} = 0.0387[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0778 + 1.96\sqrt{\frac{0.0778*0.9222}{180}} = 0.1169[/tex]

The 95% confidence interval for the overall noncompliance proportion is (0.0387, 0.1169).

Answer:

21/50

Step-by-step explanation:

Given that Jackson's sweets from last Halloween from last year was 42% chocolate, we can assume he had a total of 100 sweets.

Out of 100 sweets, 42 pieces are chocolate, so:

42/100

When simplifying this fraction into its simplest form, the most you can do is divide the numerator(top) and denominator(bottom) by 2.

Your result would be 21/50

Hope this helps!

Answer:

the number is 65.

Step-by-step explanation:

n-16=49

n=65

Therefore, the number is 65.

Answer:

slope intercept form y = m x +C

                                [tex]y = \frac{4x}{3} -\frac{40}{3}[/tex]

Step-by-step explanation:

step(i):-

Given two points are A  (7,-4) and B(-1,2)

Slope of two lines formula

 [tex]m= \frac{y_{2} -y_{1} }{x_{2} -x_{1} } = \frac{-1-7}{2-(-4)} =\frac{-8}{6} = \frac{4}{3}[/tex]

Step(ii):-

The equation of the straight line passing through the two points

                                      y-y₁ = m(x-x₁)

Let (x₁ , y₁) = (7,-4)

                                    y - (-4) =[tex]\frac{4}{3}[/tex] (x-7)

On cross multiplication , we get

                                    3(y+4) = 4(x-7)

                                    3 y +12 = 4 x -28

subtract '12' on both sides , we get

                                    3 y = 4 x -28 -12

                                     3 y = 4 x - 40

Dividing '3' on both sides, we get

Now slope intercept form y = m x +C

                                      [tex]y = \frac{4x}{3} -\frac{40}{3}[/tex]

Final answer:-

slope intercept form y = m x +C

                                [tex]y = \frac{4x}{3} -\frac{40}{3}[/tex]

Answer:

one atom of that element

Step-by-step explanation:

For example, F1 means one atom of the element Fluorine

Answer:

[tex] 75= 119 -1.96 \sigma[/tex]

[tex] \sigma = \frac{75-119}{-1.96}= 22.45[/tex]

And tha's equivalent to use this formula:

[tex] 163= 119 +1.96 \sigma[/tex]

[tex] \sigma = \frac{163-119}{1.96}= 22.45[/tex]

Step-by-step explanation:

For this case the 95%of the values are between the following two values:

(75 , 163)

And for this case we know that the variable of interest X "length of a movie" follows a normal distribution:

[tex] X \sim N( \mu, \sigma)[/tex]

We can estimate the true mean with the following formula:

[tex]\mu = \frac{75+163}{2}= 119[/tex]

Now we know that in the normal standard distribution we know that we have 95% of the values between 1.96 deviations from the mean. We can find the value of the deviation with this formula:

[tex] 75= 119 -1.96 \sigma[/tex]

[tex] \sigma = \frac{75-119}{-1.96}= 22.45[/tex]

And tha's equivalent to use this formula:

[tex] 163= 119 +1.96 \sigma[/tex]

[tex] \sigma = \frac{163-119}{1.96}= 22.45[/tex]

Answer:

It is

Step-by-step explanation:

Using Pythagoras 51^2 = 50^2 + b^2

b=10.0499  

Answer:

2. x = 11

3. x = 19

4. x = 23

5. x = 6

6. x = 10

Step-by-step explanation:

2. x + 12 =23

x = 23 - 12

x = 11

3. x - 6 = 13

x = 13 + 6

x = 19

4. x - 9 = 14

x = 14 + 9

x = 23

5. 2x = 12

x = 12/2

x = 6

6. 3x = 30

x = 30/3

x = 10

Answer:

[tex]\bar v = 60\,mph[/tex]

Step-by-step explanation:

The distance travelled by Lisa in the first four hours of her trip is:

[tex]\Delta s = \left(50\,mph)\cdot (4\,h)[/tex]

[tex]\Delta s = 200\,mi[/tex]

The distance remaining and her average speed are, respectively:

[tex]\Delta s_{R} = 440\,mi - 200\,mi[/tex]

[tex]\Delta s_{R} = 240\,mi[/tex]

[tex]\bar v = \frac{240\,mi}{4\,h}[/tex]

[tex]\bar v = 60\,mph[/tex]

Answer:

[tex]2\frac{4}{10}=\frac{24}{10}=\frac{12}{5}[/tex]

Step-by-step explanation:

Here we have a number in the ones place, 2, and a number in the tenths place, 4.

Here our whole number is 2, the numerator is 4, and it is in the tenths place, so our denominator will be 10

Our fraction becomes [tex]2\frac{4}{10}[/tex] which then turns into the improper fraction [tex]\frac{24}{10}[/tex] and then simplifying if needed becomes [tex]\frac{12}{5}[/tex] after dividing the fraction by 2

Answer:

29 miles were used per gallon

Step-by-step explanation:

257 / 9 = 28.555..

We can round 28.555 to about 29.

So John got 29 miles per gallon.

3/5 are black. To rewrite the fraction with a denominator of 100. Find how many thieves the denominator 5 goes into 100:

100/5 = 20

Multiply both the numerator and denominator by 20:

3/5 = 60/100

Answer:

Rewrite in standard form to find the center (h,k) and radius r.

Center: (−1,−2)

Radius: √6

Rewrite in standard form to find the center (h,k) and radius r.

Center: (3/2,6)

Radius: 11/2

Rewrite in standard form to find the center (h,k) and radius r.

Center: (3,−7)

Radius: 8

Rewrite in standard form to find the center (h,k) and radius r.

Center: (0,10)

Radius: 9

Rewrite in standard form to find the center (h,k) and radius r.

Center: (−4,−4)

Radius: 4√2

Answer:

33.6% of X = 26800

X = 26800 / 33.6%

   = 26800 / 0.336

  = 79762

Note the answer is rounded

Step-by-step explanation:

Answer:

1.05 radians

Step-by-step explanation:

Given that Vanessa is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the Counter Clockwise direction.

She stops skiing when she is 1.244 km to the right and 2.169 km above the center of the ski trail.

This can be represented as (1.244, 2.169) on a circle of radius 2.5 km.

From the coordinate point (1.244, 2.169) derived, x=1.244 and y=2.169.

By the definition of tangent,

[tex]\tan \theta =\frac{y}{x} \\\\\tan \theta =\dfrac{2.169}{1.244}\\\\ \theta=\arctan \dfrac{2.169}{1.244}\\\\\\ \theta=1.05006[/tex]

Vanessa swept out approximately 1.05 radians since she started skiing.