The admission fee at an amusement park is $1.50 for children and S4 for adults. On a certain day, 289 people entered the park, and the admission fees collected totaled 746.00 dollars. How many children and
how many adults were admitted?
number of children equals
number of adults equals?

Answer:

slope of the line through (3, 7) and (-1, 4) is

[tex]m = \frac{4 - 7}{ - 1 - 3} \\ \\ = \frac{ - 3}{ - 4} \\ \\ = \frac{3}{4} [/tex]

Hope this helps you

Answer:

3/4

Step-by-step explanation:

Using the slope formula

m = (y2-y1)/(x2-x1)

   = (4-7)/(-1-3)

   = -3/-4

   = 3/4

Answer:

(H1, T1)

Step-by-step explanation:

Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).

Answer:

D. (H1, T1)

Step-by-step explanation:

Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is

D. (H1, T1)

Answer:

a dilation by One-fourth and a translation

Step-by-step explanation:

For determining the sequence first we have to find out the scale factor which is shown below:

We can calculate the scale factor to obtain  

[tex]= \frac{1.5}{6} \\\\ = \frac{1}{4}[/tex]

Now as we know that the triangle XYZ and the triangle ABC are similar to each other but in the triangle XYZ is smaller in size and it is a shift to upward and right

Therefore the last option is correct

Answer:

Step-by-step explanation:

(4x³ - 5x² + 3x ) - 4(5x² - 7x³ - 8x)

Remove the brackets and simplify.

We have

4x³ - 5x² + 3x - 20x² + 28x³ + 32x

Group like terms and simplify

That's

4x³ + 28x³ - 5x² - 20x² + 3x + 32x

We have the final answer as

- 3 - ( 4x + 3y - 2z ) - 4 + 2( 5x - 4y + 6z)

Remove the brackets and simplify

That's

- 3 - 4x - 3y + 2z - 4 + 10x - 8y + 12z

Group like terms and simplify

- 4x + 10x - 3y - 8y + 2z + 12z - 3 - 4

We have the final answer as

Hope this helps you

Answer: 3

Step-by-step explanation:

7x=21 21/7=3

Answer:

work is shown and pictured

Answer:

[tex] S.A = 246.6 in^2 [/tex]

Step-by-step explanation:

The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.

Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]

Where,

B.A = Base Area of the pyramid = 9*9 = 81 in²

P = perimeter of the base = 4(9) = 36 in

L = slant height of pyramid = 9.2 in

Plug in the values into the given formula to find the surface area

[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]

[tex] = 81 + 18*9.2 [/tex]

[tex] = 81 + 165.6 [/tex]

[tex] S.A = 246.6 in^2 [/tex]

Answer:

[tex] \boxed{\sf Area \ of \ the \ rectangle = 91 \ yd^{2}} [/tex]

Given:

Length of the rectangle = 4 yd longer than its width

Perimeter of the rectangle = 36 yd

To Find:

Area of the rectangle

Step-by-step explanation:

Let the width of the rectangle be 'w' yd

So,

Length of the rectangle = (w + 4) yd

[tex] \therefore \\ \sf \implies Perimeter \: of \: the \: rectangle = 2(Length + Width) \\ \\ \sf \implies 36 = 2((4 + w) + w) \\ \\ \sf \implies 36 = 2(4 + w + w) \\ \\ \sf \implies 36 = 2(4 + 2w) \\ \\ \sf 36 =2(2w+4) \: is \: equivalent \: to \: 2(2w + 4) = 36: \\ \sf \implies 2(2w + 4) = 36 \\ \\ \sf Divide \: both \: sides \: of \: 2 (2w + 4) = 36 \: by \: 2: \\ \sf \implies 2w + 4 = 18 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies 2w = 14 \\ \\ \sf Divide \: both \: sides \: of \: 2w = 14 \: by \: 2: \\ \sf \implies w = 7[/tex]

So,

Width of the rectangle = 7 yd

Length of the rectangle = (7 + 4) yd

= 13 yd

[tex] \therefore \\ \sf Area \ of \ the \ rectangle = Length \times Width \\ \\ \sf = 7 \times 13 \\ \\ \sf = 91 \: {yd}^{2} [/tex]

Answer:

Side a^2 = 49 + 16

Side a^2 = 65

Side a = 8.062

sin (B) = 4 / 8.062

cos (B) = 7 / 8.062

tan (B) = 4 / 7

cot (B) = 7 / 4

sec (B) = 8.062 / 7

csc (B) = 8.062 / 4

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

The permutation formula is P(n, r) = n! / (n - r)!. We know that n = 7 and r = 2 so we can write:

7! / (7 - 2)!

= 7! / 5!

= 7 * 6 * 5 * 4 * 3 * 2 * 1 / 5 * 4 * 3 * 2 * 1

= 7 * 6 (5 * 4 * 3 * 2 * 1 cancels out)

= 42

Answer:

[tex]\boxed{42}[/tex]

Step-by-step explanation:

Apply the permutation formula.

[tex]P(n,r)=\frac{n!}{ (n-r)!}[/tex]

[tex]P=number \: of \: permutations\\n=total \: number \: of \: objects \: in \: the \: set\\r=number \: of \: choosing \: objects \: from \: the \: set\\[/tex]

[tex]n=7\\r=2[/tex]

Plug in the values and evaluate.

[tex]P(7,2)=\frac{7!}{ (7-2)!}[/tex]

[tex]P(7,2)=\frac{7!}{ (5)!}[/tex]

[tex]P(7,2)=\frac{5040}{120}[/tex]

[tex]P(7,2)=42[/tex]

Answer:

A

Step-by-step explanation:

[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]

Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.

Add the top and bottom numbers together, divide that by 2 then multiply by the height.

15.3 + 19.5 = 34.8

34.8/2 = 17.4

17.4 x 11.1 = 193.14

Answer is 193.1 m^2

Answer:

hello :- 9/7 and 3/8

Step-by-step explanation:

y = 6(7x + 9)(8x – 3)

y=0 means :   7x+9=0   or 8x-3=0

7x = -9  or 8x=3

x= - 9/7   or x= 3/8

Answer:

-9/7, 3/8

Step-by-step explanation:

The zeroes can be found in the parenthesis.

You need to set each parenthesis to zero first.

7x+9=0

subtract 9

7x=-9

divide 7

x=-9/7

For 8x-3=0

add the 3

8x=3

divide the 8

x=3/8

Answer:

The dentist should fail to reject the Null hypothesis

Step-by-step explanation:

From the question we are told that

       The sample size is  n =  400

       The  sample  mean is  [tex]\= x = 149[/tex]

       The  level of significance is  5%  = 0.05  

       The  Null hypothesis is  [tex]H_o : p = 0.40[/tex]

        The Alternative  hypothesis is  [tex]H_a : p < 0.40[/tex]

         The  p-value is  [tex]p-value = 0.131[/tex]

Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis  

Answer:

Dian has $250 originally.

Step-by-step explanation:

Let the total money Dian has originally = $S

Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,

Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]

Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]

                                   = [tex]\frac{\text{5S-2S}}{5}[/tex]

                                   = [tex]\frac{3S}{5}[/tex]

Since Dian has $150 left then the equation will be,

[tex]\frac{3S}{5}=150[/tex]

S = [tex]\frac{150\times 5}{3}[/tex]

S = $250

Therefore, Dian has $250 originally.

Answer:

x = 3 ± sqrt(11)

Step-by-step explanation:

x^2 - 6x + 9 = 11

Recognizing  that this is a perfect square trinomial

(x-3) ^2 =11

Taking the square root of each side

sqrt((x-3) ^2) = ± sqrt(11)

x-3 =± sqrt(11)

Add 3 to each side

x = 3 ± sqrt(11)

Answer:

[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]

Step-by-step explanation:

Hello,

   [tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]

Do not hesitate if you have any question

Hope this helps

Answer:

see explanation

Step-by-step explanation:

Pythagorean Theorem

7² + 8² = x²

49 + 64 = x²

113 = x²

x = √113 or 10.63

Distance Formula

√(-4 - 4)² + (4 - -3)²

= √8² + 7²

= √113 or 10.63

Answer:

A. 0.89.

Step-by-step explanation:

The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.

The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.

From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.

the bag is 200g

total weight with oranges is 1400g

deduct the bags weight from total weight

1400 - 200

1200g

this is the weight of the three oranges

so each orange would be

1200 ÷ 3

400g

Answer:

D.

m = 2 = figures/month

b = 20 = # of action figures

Answer:

n = 17

Step-by-step explanation:

Assuming

- probability of success (making free throw) does not vary

We have

n = 17 (trials)

p = 0.479

x > 9

The answer is "[tex]\bold{p(x>9)=0.2550319}[/tex]"

[tex]\to X:[/tex] Number of creating free throws in a set [tex]\bold{17\ \ x \sim bin(17,0.479)}[/tex]

Know we calculating the P(makes more than 9 of them)

[tex]=\bold{9(X>9)=1-P(Z<=9)}[/tex]

Using the R-code:

[tex]\to \bold{1-p\ binom(9,17,0.479)}\\\\\to \bold{[1]0.2550319}\\\\\bold{\therefore}\\\\ \to \bold{p(x>9)=0.2550319}[/tex]

Learn more:

binomial distribution: brainly.com/question/9065292

Answer:

-3a

Step-by-step explanation:

3(-a)

Expand brackets.

3 × -1a

-3a

Answer:

[tex]\large \boxed{\text{5.29 s}}[/tex]

Step-by-step explanation:

The appropriate free fall equation is  

y = v₀t + ½gt²

Data:

v₀ = 0

g = 32.17 ft·s⁻²

Calculation:

[tex]\begin{array}{rcl}450 &=& v_{0}t + \dfrac{1}{2}gt^{2}\\\\& = & 0 \times t + \dfrac{1}{2}\times 32.17t^{2}\\\\& = & 16.08t^2\\t^{2}& = & \dfrac{450}{16.08}\\\\& = & 27.97\\t & = & \textbf{5.29 s}\\\end{array}\\\text{It took $\large \boxed{\textbf{5.29 s}}$ for the phone to reach the ground.}[/tex]

Answer:

They are not parallel because their slopes are not equal

Step-by-step explanation:

From the diagram attached, The line PQ has point P at (-5, 3) and point Q at (5, 1).

For line RS, point R is at (-4, -2) and point S is at (0, -4).

Two lines AB and CD are said to be parallel to each other if they have the same slope, i.e if the slope of AB is m1 and the slope of CD is m2, m1 = m2. When two lines are parallel, they can never intersect.

The slope (m) of of a line given two points on the line is calculated using:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

For line PQ has point P at (-5, 3) and point Q at (5, 1), the slope is given as:

[tex]m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{1-3}{5-(-5)}=-\frac{1}{5}\\[/tex]

For line RS, point R is at (-4, -2) and point S is at (0, -4), the slope is given as:

[tex]m_2=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-(-2)}{0-(-2)}=-1[/tex]

Since the slope of PQ (-1/5) and the slope of line RS (-1)  are not equal, therefore the lines are not parallel

Answer:

They are not parallel because their slopes are not equal.

Step-by-step explanation:

The first person to answer this was correct, please mark them brainliest.

Answer:

Hope this is correct

HAVE A GOOD DAY!

Answer:

the probability that the company's total hospital costs in a year are less than 50,000  = 0.7828

Step-by-step explanation:

From the given information:

the probability that the company's total hospital costs in a year are less than 50,000 will be the sum of the probability of the employees admitted.

If anyone is admitted to the hospital, they have [tex]\dfrac{1}{3}[/tex] probability of making at least one more visit, and a [tex]\dfrac{2}{3}[/tex]  probability  that this is their last visit.

If zero employee was admitted ;

Then:

Probability = (0.80)⁵

Probability = 0.3277

If one employee is admitted once;

Probability = [tex](0.80)^4 \times (0.20)^1 \times (^5_1) \times (\dfrac{2}{3})[/tex]

Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{2}{3})[/tex]

Probability = 0.2731

If one employee is admitted twice

Probability = [tex](0.80)^3 \times (0.20)^2 \times (^5_2) \times (\dfrac{2}{3})^2[/tex]

Probability = [tex](0.80)^3 \times (0.20)^2 \times (\dfrac{5!}{(5-2)!}) \times (\dfrac{2}{3})^2[/tex]

Probability = 0.1820

If two employees are admitted once

Probability = [tex](0.80)^4\times (0.20)^1 \times (^5_1) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]

Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]

Probability = 0.0910

∴

the probability that the company's total hospital costs in a year are less than 50,000  = 0.3277 + 0.2731 + 0.1820

the probability that the company's total hospital costs in a year are less than 50,000  = 0.7828

Answer:

The  probability is  [tex]P(X < 900 ) = 0.0918[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 1100[/tex]

    The  standard deviation is  [tex]\sigma = 150[/tex]

     The random number value is  x =900

The probability that a trainee earn less than 900 a month is mathematically represented as

       [tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]

Generally the z-value for the normal distribution is mathematically represented as

       [tex]z = \frac{x -\mu }{\sigma }[/tex]

So From above we have

      [tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]

      [tex]P(X < 900 ) = P( Z <-1.33)[/tex]

Now from the z-table

    [tex]P(X < 900 ) = 0.0918[/tex]

Answer:

84%

Step-by-step explanation:

We find the z-score here

z= x-mean/SD = 32-40/8 = -1

So the probability we want to find is;

P(z>-1)

This can be obtained using the standard score table

P(z>-1) = 0.84 = 84%

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The  standard deviation is  [tex]\sigma = 2.45[/tex]  

Step-by-step explanation:

From the given data we can compute the expected mean for each random values as follows

          [tex]E(X) = \sum [ X * P(X = x )]\\\\ X \ \ \ \ \ \ X* P(X =x )\\ 0 \ \ \ \ \ \ \ \ \ \ 0* 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2 * 0.3 = 0.6 \\ 4 \ \ \ \ \ \ \ \ \ \ 4 * 0.2 = 0.8\\ 6 \ \ \ \ \ \ \ \ \ \ 6* 0.1 = 0.6[/tex]

So  

          [tex]E(x) = 0 + 0.6 + 0.8 + 0.6[/tex]

          [tex]E(x) = 2[/tex]

The  

             [tex]E(X^2) = \sum [ X^2 * P(X = x )]\\\\ X \ \ \ \ \ \ \ \ \ \ X^2 * P(X=x ) \\ 0 \ \ \ \ \ \ \ \ \ \ 0^2 * 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2^2 * 0.3 = 12 \\ 4 \ \ \ \ \ \ \ \ \ \ 4^2 * 0.2 = 3.2 \\ 6 \ \ \ \ \ \ \ \ \ \ 6^2 * 0.1 = 3.6[/tex]

So  

        [tex]E(X^2) = 0 + 1.2 + 3.2 + 3.6[/tex]

        [tex]E(X^2) = 8[/tex]

Now  the variance is  mathematically evaluated as

         [tex]Var (X) = E(X^2 ) -[E(X]^2[/tex]

Substituting value  

        [tex]Var (X) = 8-4[/tex]

        [tex]Var (X) = 6[/tex]

The standard deviation is mathematically evaluated as

       [tex]\sigma = \sqrt{Var(x)}[/tex]

      [tex]\sigma = \sqrt{4}[/tex]

      [tex]\sigma = 2[/tex]

Answer:

woman is 37, girl is 7

Step-by-step explanation:

7(x-2) = y-2

4(x+3) = y+3

7x - 14 = y - 2

7x - 12 = y

4x + 9 = y

3x - 21 = 0

x = 7

y = 37