An after-school care facility tries to maintain a 2-to-1 ratio of children to adults. If the facility hired five adults, what is the maximum number of children that can enroll?

Hi there! :)

Answer:

Given the information, we can write an equation in slope-intercept form

(y = mx + b) to graph the line:

Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the

x-coordinate given for 'x':

-4 = -2/3(-7) + b

-4 = 14/3 + b

Solve for b:

-12/3 = 14/3 + b

-12/3 - 14/3 = b

-26/3 = b

Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)

Some points on the line include:

(-7, -4)

(-4, -6)

(0, -26/3)

(2, -10)

(5, -12)

Answer:

18

Step-by-step explanation:

Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.

Answer:

vol = 96

Step-by-step explanation:

Area of a triangle = 1/2 * b * h

b = 4

h = 6

A = 0.5 * 4 * 6

A = 12

length = 8

vol = Area * length

vol = 12 * 8

vol = 96

Answer:

(104 + 16 sqrt 13)

Step-by-step explanation:

i did this on my school, it was correct

Answer:

Angle BCA = 70

Angle CAB = 20

Step-by-step explanation:

Not sure what angle you meant, so I'll give you all of them <3

Angle BCA = 70 degrees, because If two angles form a line, they add up to 180.  (110+x=180, x = 70)

Angle CAB = 20 degrees, because there are 180 degrees in a triangle, so 90+70+x=180, x = 20

Hope it helps <3

Answer:

BCA = 70

CAB = 20

ABC=90

Step-by-step explanation:

ABC is 120 because the square indicates that

BCA = 70 because angles on a straight line add up to 180.

110+x=180

x=180-110

=70

Angle CAB = 20 degrees, because angles in a triangle add up to 180

90+70+x=180

x = 180-(90+70)

=180-160

=20

Please mark as brainliest

Answer:

i think it is c. i may be incorrect, i am sorry!

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I did the math

Answer:

Convenience sampling.

Step-by-step explanation:

To gather information on customer satisfaction, a researcher goes into each store and interviews six randomly selected customers at each store. This sampling technique is called convenience sampling.

Convenience sampling can be defined as a sampling method which involves the researcher selecting or collecting data that is easily available or choosing the individuals who are easiest to reach in a population. It is a type of non-probability method of sampling where the first or easiest available data source is being used by the researcher without other requirements.

In this scenario, to gather information on customer satisfaction, the researcher went to the store most likely situated in a shopping mall to collect data from six (6) customers in each stores.

Some of the advantages of convenience sampling are low cost, data are collected quickly, lesser rules etc.

Answer: See answer in the attached file

Step-by-step explanation:

Answer: 1unit.

Step-by-step explanation:

Area of the rectangle

A = length × width

Since the area = 20 and the width is x and the length is x + 1.

We now substitute for the values in the above formula and solve for x

20 = x × x + 1

20 = x( x + 1 ), we now open

20 = x² + x , then re arrange.

x² + x - 20 = 0, this is a quadratic equation.we solve for x using quadratic means

Here, I am going to solve using factorization by grouping

x² + x - 20 = 0

x² + 5x - 4x - 20 = 0

x( x + 5 ) - 4( x + 5 ) = 0

( x + 5 )( x - 4 ). = 0

Therefore, the solution for x will be

x = -5 or 4, but x can not be -5 ( negative), so x = 4.

Now the difference between width and the length can easily be calculated from the above,

Width = 4 (x) , and length = 5 (4 + 1),

Now difference will be

5 - 4 = 1unit.

Answer:

Step-by-step explanation:

The happiest used in a test in statistics are the null and the alternative hypothesis. The null hypothesis is usually the default statement while the alternative hypothesis is thevopposite of the null hypothesis.

In this case study, the null hypothesis is u1 = u2: the average mean time it takes to accelerate to 30 miles per hour for car 1 is the same as that for car 2.

The alternative hypothesis is u1 > u2: the mean time it takes to accelerate to 30 miles per hour is greater than that for car 2 thus car 1 is slower to accelerate as it takes more time.

Answer:

AGE = 129 degrees

Step-by-step explanation:

Two angles whose sum is 180° are called supplementary angles. The measure of ∠AGE in the given figure is 129°.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

In the given figure, line segment CE is a straight line. Therefore, the sum of the angles formed on the same side of the line will be a linear pair.

Thus, the measure of the angles can be rewritten as,

∠AGC + ∠AGE = 180°

51° + ∠AGE = 180°

∠AGE = 180° - 51°

∠AGE = 129°

Learn more about Supplementary Angles:

https://brainly.com/question/2882938

#SPJ2

Answer:

Type I error: Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.

Type II error: Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.

Step-by-step explanation:

We are given the following hypothesis below;

Let p = proportion of people who write with their left hand

Null Hypothesis, [tex]H_0[/tex] : p = 0.18      {means that the proportion of people who write with their left hand is equal to 0.18}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.18      {means that the proportion of people who write with their left hand is different from 0.18}

Type I error states that we would reject the null hypothesis given the fact that the null hypothesis was actually true. Or in other words, the probability of rejecting a true hypothesis.

So, according to our question, Type I error is to Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.

Type II error states that we would accept the null hypothesis given the fact that the null hypothesis was actually false. Or in other words, the probability of accepting a false hypothesis.

So, according to our question, Type II error is Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.

Answer:

41 and 11.

Step-by-step explanation:

Let's say the 2 numbers are x and y.

Since they add up to 52, x + y = 52.

Seeing as the difference is 30, x - y = 30 assuming x is the larger number.

We have left:

x + y = 52

x - y = 30

By solving these simultaneous equations (adding the 2 equations together for instance), we are left with 2x = 82

Therefore x = 41.

Since x + y = 52

41 + y = 52

Therefore y = 11

Therefore we have: the larger number is 41 and the smaller number is 11.

In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.

Answer:

[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]

First answer is correct.

Step-by-step explanation:

we know that,

[tex] {x}^{a} = {x}^{b} [/tex]

[tex]a = b[/tex]

So, according to that,

[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]

Therefore,

[tex]2x - 1 = 5x - 14[/tex]

Answer:

When Ø = 300°, Ø = 60 degrees.

When Ø = 225°, Ø = 45 degrees.

When Ø = 480°, Ø = 60 degrees.

When Ø = -210°, Ø = 30 degrees.

Step-by-step explanation:

Reference angles are in Quadrant I (0° to 90°).

1. Find 300° (Quadrant IV) on the unit circle. Since it's in Quadrant IV, you use 360 - 300 = 60° to get your answer.

2. Find 225° (Quadrant III) on the unit circle. Since it's in Quadrant III, you use 225 - 180 = 45° to get your answer.

3. The angle 480° is not on the unit circle. To find its corresponding angle between 0° and 360°, use 480 - 360 = 120°. Then, find 120° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 120 = 60° to get your answer.

4. The angle -210° is not on the unit circle. To find its corresponding angle between 0° and 360°, use -210 + 360 = 150°. Then, find 150° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 150 = 30° to get your answer.

Answer:

C = $6050

Equation:

To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:

[tex]3500+150(S)=C[/tex]

3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.

Solving the equation

To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.

[tex]3500+150(17)=C[/tex]

150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.

Our answer is: C = $6050

Answer:  without trying each calculation individually,  6750 4-digit numbers are not divisible by 4

Step-by-step explanation:  From 1000 to 9999 there are 9000 4-digit numbers 9999 - 999 = 9000.

Eliminate all the odd numbers 9000/2 = 4500

Eliminate the even numbers divisible by 2 but not by 4. 4500/2 = 2250

9000 - 2250 = 6750.

Answer:

[tex]\huge\boxed{x=\sqrt{21}}[/tex]

Step-by-step explanation:

ΔABD and ΔBCD are similar (AAA).

Therefore the corresponding sides are in proportion:

[tex]\dfrac{BD}{CD}=\dfrac{AD}{BD}[/tex]

Substitute

[tex]BD=x;\ CD=3;\ AD=7[/tex]

[tex]\dfrac{x}{3}=\dfrac{7}{x}[/tex]              cross multiply

[tex](x)(x)=(3)(7)\\\\x^2=21\to x=\sqrt{21}[/tex]

Answer:

x=60

Step-by-step explanation:

This is an equilateral triangle which means all the sides are equal.

If all the sides are equal then all the angles are equal

180/3 = 60

x=60

Answer:

x= 60°

Step-by-step explanation:

We can tell that both of these triangles are equilateral. We can tell because all of their sides have little tick marks, meaning that they are all equal, meaning that the triangle is equilateral. In an equilateral triangle, we know that through definitions all of the angles are equal to 60°. Since y is an angle inside of an equilateral triangle, it is equal to 60°

Answer:

8 hours

1 hour

8 hours

0.288675

Step-by-step explanation:

We complete the answer as follows;

mu = mean = 8 hours

sigma = standard deviation= 1 hour

Mu_x bar = mu = 8 hours

sigma_x bar = sigma/√(n) = 1/√(12) = 0.288675

Answer:

A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Step-by-step explanation:

As we know that

The standard deviation is the square root of the variance and on the other side the variance is the square of the standard deviation

In mathematically

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

And,

[tex]variance = \sigma^2[/tex]

Moreover, the standard deviation and the variance could never by negative neither the squared deviation is negative. All three are always positive

Hence, the correct option is a.

Answer:

B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Answer:

True

Step-by-step explanation:

Answer:

[tex]x= \frac{5^{14}+3}{2}[/tex]

Step-by-step explanation:

The correct steps to solve the equation are:

[tex]14=log_5(2x-5)[/tex]

[tex]5^{14}=5^{log_5(2x-3)}[/tex]

Because [tex]a^{log_am}=m[/tex]

So, solving we get:

[tex]5^{14}=2x-3[/tex]

Sum 3 on every side:

[tex]5^{14}+3=2x-3+3\\5^{14}+3=2x[/tex]

Dividing by 2 into both sides:

[tex]\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x[/tex]

So, the answer is  [tex]x= \frac{5^{14}+3}{2}[/tex]

Answer: Step 2

Step-by-step explanation:

This is correct according to Edge 2021

Answer:

40%

Step-by-step explanation:

1299-725= 574

574/1299 x 100 = 44.19%

The rate of discount on the dinette set = 44.2%.

Often, goods are sold at a price that is lower than their marked price. The price at which the good is sold is called the selling price and the difference between the marked price and the selling price is the discount.

Discount = Marked Price - Selling Price.

Rate of Discount = Discount/Marked Price * 100%.

In the question, we are given that Stella bought a dinette set on sale for $725. The original price was $1,299.

We are asked to calculate the rate of discount on the dinette set.

The marked price of the dinette set = $1299.

The selling price of the dinette set = $725.

∴ The discount on the dinette set = the marked price of the dinette set - the selling price of the dinette set = $1299 - $725 = $574

∴ The rate of discount on the dinette set = the discount on the dinette set/the marked price of the dinette set *100%

or, The rate of discount on the dinette set = 574/1299 * 100%

or, The rate of discount on the dinette set = 0.4418 * 100%

or, The rate of discount on the dinette set = 44.18% ≈ 44.2% (to the nearest tenth of a percent)

∴ The rate of discount on the dinette set = 44.2%.

Learn more about the rate of discount at

https://brainly.com/question/7459025

#SPJ2

Answer:

Option (B)

Step-by-step explanation:

If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.

Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]

a + c = 172°

Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.

Therefore, a = c

⇒ a = c = 86°

Therefore, a = 86°

Option (B) will be the answer.

Rewrite the limit as

[tex]\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}[/tex]

Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get

[tex]\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}[/tex]

Answer:

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

Step-by-step explanation:

Using the fundamental theorem of calculus

Taking the derivative of the integral gives back the function

Since the lower limit is a constant when we take the derivative it is zero

d/dx [tex]\int\limits^x_4 {g(t)} \, dt = g(x)[/tex]

g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))

Replacing t with x

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

Answer: [tex]\dfrac{1}{56}[/tex]

Step-by-step explanation:

Total horses = 6

Number of ways to choose top 3 finishers in order = 3! = 6

Number ways to select 3 horses out of 8 in order = [tex]^8P_3[/tex]  [By permutations]

[tex]=\dfrac{8!}{(8-3)!}=\dfrac{8!}{5!}=8\times7\times6=336[/tex]

Now, the probability that the gambler will win his bet =

[tex]\dfrac{\text{Number of ways to choose top 3 finishers }}{\text{Number ways to select 3 horses out of 8 in order}}[/tex]

[tex]=\dfrac{6}{336}\\\\=\dfrac{1}{56}[/tex]

Hence, the required probability =  [tex]\dfrac{1}{56}[/tex]

Answer:

All real numbers except for 5.

Step-by-step explanation:

[tex]f(x)=\frac{x}{x-5}[/tex]

The domain of rational functions is determined by the denominator. The denominator cannot equal zero since if they do, the function will be undefined.

Thus, we need to find the zero(s) of the denominator to determine the domain.

[tex]x-5=0[/tex]

[tex]x=5[/tex]

Therefore, the domain of the rational function is all real numbers except for 5.

In set builder notation, this is:

[tex]\{x|x\in \mathbb{R}, x\neq 5\}[/tex]

Answer: B. Perpindicular Bisector.

Step-by-step explanation:

BD is a perpindicular bisector because it splits CE into 2 equal segments via a right angle.

Answer:

midsegement

Step-by-step explanation: