At a conference, there are 121 math teachers and 11 science teachers. Write the
ratio of math teachers to science teachers in simplest form.

Answer:

10 meters

Step-by-step explanation:

The triangles are similar, by a scale factor of 2, so if QR is 10, then ST is 1/2 or 5

We can use trig functions to find SP

sin P = opp/ hyp

sin 30 =5/SP

SP sin 30 =5

Divide each side by sin 30

SP = 5 / sin 30

SP =10

Answer:

C. 10 meters

Step-by-step explanation:

sin(30) = QR/QP

½ = 10/QP

QP = 20

PS = ½ × 20

PS = 10

The equation is [tex]-\frac{1}{2} x+3[/tex]

This is what you should input in the chart:

(0,3)

(3,2)

(6,1)

(9,0)

(12,-1)

(15,-2)

Answer:

  1520.5 ft²

Step-by-step explanation:

A diagram can be helpful.

The total area is the sum of ...

  3/4 of a circle with radius 24 ft

  1/4 of a circle with radius 12 ft

  1/4 of a circle with radius 8 feet

__

The area of a whole circle is given by ...

  A = πr²

so our grazing area is ...

  A = (3/4)π(24 ft)² + (1/4)π(12 ft)² + (1/4)π(8 ft)²

  = π(432 ft² +36 ft² +16 ft²) = 484π ft²

  A ≈ 1520.5 ft²

Answer:

30 years old now

Step-by-step explanation:

Add the years to her age then to determine her age now

11+19 = 30

She is 30 years old now

The pretax cost of debt is 5.43% and the aftertax cost of debt is 4.24%.

To calculate the pretax cost of debt, we need to find the current yield of the bond. The current yield is the annual coupon payment divided by the market price. In this case, the coupon rate is 5% and the market price is 92% of the face value. Therefore, the current yield is (0.05 * face value) / (0.92 * face value), which simplifies to 0.0543 or 5.43%.

To calculate the aftertax cost of debt, we need to multiply the pretax cost of debt by (1 - tax rate). In this case, the tax rate is 22%. Therefore, the aftertax cost of debt is 5.43% * (1 - 0.22), which simplifies to 4.24%.

https://brainly.com/question/32690229

#SPJ3

Answer:

x = -10.

Step-by-step explanation:

x / 10 = -1

To solve the equation we isolate the x on one side.

Whatever operation we do one one side of the equation we have to do the same on the other side so that the balance is maintained.

Here to isolate x we multiply both sides by 10:

x

--    * 10   =  -1 * 10

10

x = -10.

Hope this helps.

Answer:

The maximum is P=112.4 at (23.4,7)

Step-by-step explanation:

From the graph, the coordinates of the vertices of the feasible region are:

(0,25)

(9,7)

(23.4, 7)

(15,17.5)

Substituting these values in the objective function, P.

At (0,25), P = 6x − 4y=6(0)-4(25)=-100

At (9,7), P = 6x − 4y=6(9)-4(7)=26

At (23.4,7), P = 6x − 4y=6(23.4)-4(7)=112.4

At (15,17.5), P = 6x − 4y=6(15)-4(17.5)=20

Since the objective is to maximize,

The maximum is P=112.4 at (23.4,7)

To solve the linear programming problem, graph the inequalities to find the feasible region, then compute the function P = 6x − 4y at each corner point of the feasible region to find the maximum value. The values of x and y must also uphold all the inequalities.

The subject of the problem is a linear programming problem, and to solve it, we first identify the feasible region by graphing inequalities. This involves graphing x + 2y ≤ 50, 5x + 4y ≤ 145, 2x + y ≥ 25, y ≥ 7, and x ≥ 0. The feasible region would be formed by the area enclosed within those lines.

Next, we find the corner points of the feasible region because, in a linear programming problem, the maximum and minimum always occur at the vertices or corner points. Let's calculate these corner points.

Finally, we evaluate the function P = 6x − 4y at each corner point and find the value of P that would be maximized. It's crucial to remember that the values of x and y must satisfy all the given inequalities.

https://brainly.com/question/34674455

#SPJ11

The standard error of the mean pertains to the variability of the mean between different samples, rather than the variability of individual measurements. Therefore, the correct interpretation is D. The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm.

The most accurate interpretation for the standard error of the mean in the context of the given problem is: D. "The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm".

The standard error of the mean (SEM) demonstrates the standard deviation of the sampling distribution of the means. It measures how far the sample mean of the data is likely to be from the true population mean. SEM gives us an estimate of the precision of our sample mean in relation to the true population mean. It's important to recognize that SEM is not about the dispersion of individual measurements, but rather about the dispersion of sample means.

https://brainly.com/question/14524236

#SPJ6

Answer 2 dollars a ride.

Step-by-step explanation:

26=50-12x

x=2

x

Answer:

the circumference decreases by a factor 1/3.

Step-by-step explanation:

Answer:

A: The circumference decreases by a factor of One-third

Answer:

-288

Step-by-step explanation:

-18*16

cause its going by 16's

pls mark me brainliest

a23 = -288

As the sequence is going by [tex]16[/tex].

∴ [tex]-18[/tex] × [tex]16=-288[/tex]

Therefore, [tex]a23=-288[/tex].

Know more about sequence here:

https://brainly.com/question/6561461

#SPJ2

Answer:

answer 1

Step-by-step explanation:

Answer:A

Step-by-step explanation:

Answer:

Anonymous simulation would be used to determine a game of darts.

The simulation which can be used to determine the game of darts is anonymous simulation.

Dart game is a game which is played in real by throwing darts over the dart boards which has to be pointed at a fixed places which gives the points.

Simulation games are the games which aims in designing the game as a context of various real life activities.

It aims in helping the real world to train, analyze and predict things in a way of entertainment.

The simulator which can be used to determine the game of darts is anonymous simulator.

Hence the description of the simulator which can be used to determine a game of darts is anonymous simulator.

To learn more about Simulators, click on the link given below :

https://brainly.com/question/17545219

#SPJ3

Answer:

The GCF is 6n^3

Step-by-step explanation:

Answer:

6.7%

Step-by-step explanation:

In this question, we are to calculate the percentage error in in the average polling results calculated.

Firstly, what this means is that we calculate the average of the total votes.

That would be ; (66 + 56 + 55 + 60 + 63)/5 =

300/5 = 60%

we now proceed to calculate the percentage error in the company’s result.

Mathematically;

percentage error = (Actual value - expected value)/expected value * 100%

Here the actual value is 64% and the expected is 60%

% error = (64-60)/60 * 100 = 4/60 * 100 = 6.67%

This is 6.7% to the nearest tenth of a percent

Answer:

The answer to your question is the letter C. 13248 square units

Step-by-step explanation:

Data

Right triangle                      Rectangle

short leg = 69                     base = x + 100

hypotenuse = 115

Process

1.- Calculate the long leg of the right triangle.

       c² = a² + b²

       b² = c² - a²

       b² = 115² - 69²

       b² = 13225 - 4761

       b² = 8464

       b = 92

2.- Calculate the length of the base of the rectangle

       base = 92 + 100

       base = 192

3.- calculate the area of the rectangle

       Area = 192 x 69

                = 13248 square units

Answer:

D. A weakness can be turned to strength

Answer:

d

Step-by-step explanation:

Answer:

No, we can't reject [tex]H_0[/tex] at the α = 0.01 level of significance.

Step-by-step explanation:

We are given the sample of five matched pairs below ;

Sample 1 (B) :    20, 20, 23, 18, 22

Sample 2 (A) :   23, 16, 15, 14, 18

Let [tex]\mu_1[/tex] = population mean for first sample

[tex]\mu_2[/tex] = population mean for second sample

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_D[/tex] = 0    {means that there is no difference between the population means of both samples}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_D[/tex] > 0    {means that three is positive difference between the population means of both samples, i.e. population mean of first sample is higher than the population mean of second sample}

The test statistics that will be used here is Paired data test statistics;

                      T.S.  = [tex]\frac{\bar D-\mu_D}{\frac{s_D}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar D[/tex] = [tex]\bar B -\bar A[/tex] = 20.6 - 17.2 = 3.4

           [tex]s_D=\sqrt{\frac{\sum D_i^{2}-n \bar D^{2} }{n-1}}[/tex]  =  [tex]\sqrt{\frac{121-5 \times 3.4^{2} }{5-1}}[/tex] = 3.975

             n = sample size = 5

So, test statistics  =  [tex]\frac{3.4-0}{\frac{3.975}{\sqrt{5} } }[/tex]  ~ [tex]t_4[/tex]     

                               =  1.913

Now at 0.01 significance level, the t table gives critical value of 3.747 at 4 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 3.747 > 1.913, 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 there is no difference between the population means of both samples.

Answer:

No, we can't reject  at the α = 0.01 level of significance.

Step-by-step explanation:

the other response is right

Though there are multiple solutions to the given equation, the two ordered pairs that are solutions would be both (1, 2) and (2, 4).

Hope this helps!

Answer:

103.62

Step-by-step explanation:

[tex]C = \pi d\\3.14 * 33 =103.62[/tex]

Answer:4

Step-by-step explanation: Odd 5/4 and 10/8 are both equal

Answer:

Your answer should be 4...

Step-by-step explanation:

In the first time you planted, you planted 10 total bulbs, and 8 of them bloomed. That means that 80% of the bulbs that you planted bloomed. So if you plant 5 more bulbs, theoretically your answer should be 4, since 80% of 5 is 4.

I'm sorry if this answer isn't a lot of help, there isn't a lot of information to go off of.

Answer: 18.1 inches

Step-by-step explanation: A volleyball is spherical in shape, and the surface area of a sphere is giving by the formula

from the data giving, the surface area was calculated to be 227 square inches. from the above formula, we define the radius, r to be the subject of formula, we arrive at

if we substitute for the surface area, we arrive at

Hence the radius of the volleyball will be 18.1 inches  

Hope this helps

Answer:

Probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career is 0.0688.

Step-by-step explanation:

We are given that a survey of students at a large university found that 82% had purchased textbooks from an off-campus vendor at least once during their college career.

Also, 45 students are randomly sampled.

Let [tex]\hat p[/tex] = sample proportion of students who have purchased textbooks from an off-campus vendor at least once during their college career.

The z-score probability distribution for sample proportion is given by;

                               Z = [tex]\frac{\hat p- p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion = [tex]\frac{40}{45}[/tex] = 0.89

p = population proportion of students who had purchased textbooks from an off-campus vendor at least once during their college career = 82%

n = sample of students = 45

Now, probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.89)

      P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.89) = P( [tex]\frac{\hat p- p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.89-0.82}{\sqrt{\frac{0.89(1-0.89)}{45} } }[/tex] ) = P(Z [tex]\geq[/tex] 1.50) = 1 - P(Z < 1.50)

                                                                      = 1 - 0.9332 = 0.0688

The above probability is calculate by looking at the value of x = 1.50 in the z table which ha an area of 0.9332.

Therefore, the required probability is 0.0688.

Noticing that there is a pattern of repetition in the question (the numbers are repeated twice), we are assuming that the mean number of words per minute is 88, the standard deviation is of 14 WPM, as well as the number of sixth graders is 137, and that there is a need to estimate the probability that the sample mean would be greater than 89.87.

Answer:

"The probability that the sample mean would be greater than 89.87 WPM" is about [tex] \\ P(z>1.56) = 0.0594[/tex].

Step-by-step explanation:

This is a problem of the distribution of sample means. Roughly speaking, we have the probability distribution of samples obtained from the same population. Each sample mean is an estimation of the population mean, and we know that this distribution behaves normally for samples sizes equal or greater than 30 [tex] \\ n \geq 30[/tex]. Mathematically

[tex] \\ \overline{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex] [1]

In words, the latter distribution has a mean that equals the population mean, and a standard deviation that also equals the population standard deviation divided by the square root of the sample size.

Moreover, we know that the variable Z follows a normal standard distribution, i.e., a normal distribution that has a population mean [tex] \\ \mu = 0[/tex] and a population standard deviation [tex] \\ \sigma = 1[/tex].

[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]

From the question, we know that

We also know the size of the sample for this case: [tex] \\ n = 137[/tex] sixth graders.

We need to estimate the probability that a sample mean being greater than [tex] \\ \overline{X} = 89.87[/tex] WPM in the distribution of sample means. We can use the formula [2] to find this question.

The probability that the sample mean would be greater than 89.87 WPM

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

[tex] \\ Z = \frac{89.87 - 88}{\frac{14}{\sqrt{137}}}[/tex]

[tex] \\ Z = \frac{1.87}{\frac{14}{\sqrt{137}}}[/tex]

[tex] \\ Z = 1.5634 \approx 1.56[/tex]

This is a standardized value and it tells us that the sample with mean 89.87 is 1.56 standard deviations above the mean of the sampling distribution.

We can consult the probability of P(z<1.56) in any cumulative standard normal table available in Statistics books or on the Internet. Of course, this probability is the same that [tex] \\ P(\overline{X} < 89.87)[/tex]. Then

[tex] \\ P(z<1.56) = 0.94062 \approx 0.9406[/tex]

However, we are looking for P(z>1.56), which is the complement probability of the previous probability. Therefore

[tex] \\ P(z>1.56) = 1 - P(z<1.56) = 1 - 0.9406[/tex]

[tex] \\ P(z>1.56) = P(\overline{X}>89.87) = 0.0594[/tex]

Thus, "The probability that the sample mean would be greater than 89.87 WPM" is about [tex] \\ P(z>1.56) = 0.0594[/tex].

Answer:

37 students

Step-by-step explanation:

Final answer:

To determine the number of students on the trip, multiply the number of adults by their ticket cost, subtract this from the total cost, and then divide the remainder by the student ticket cost to find that 37 students went on the trip.

Explanation:

The question involves a group pricing problem where the wildlife club spent $350 on zoo admission, adults tickets cost $7.50 each, and student tickets cost $5 each. If there were 22 adults on the trip, we need to calculate the number of students who attended.

To solve this, we first calculate the total cost for adult admissions by multiplying the number of adults by the cost per adult ticket: 22 adults × $7.50/adult = $165. Then, we subtract this amount from the total cost to determine the amount spent on student tickets: $350 total - $165 for adults = $185 for students.

Finally, we divide the remaining amount by the cost per student ticket to find the number of student tickets: $185 ÷ $5/student = 37 students. Therefore, 37 students went on the trip.

Step-by-step explanation:

1/3 πr²h

Given

diameter (d) = 8ft

radius (r) = d/2 = 8/2 = 4 ft

height (h) = 3 ft

Volume of cone

[tex] \frac{1}{3} \times \pi {r}^{2} h[/tex]

[tex] \frac{1}{3} \times 3.14 \times {4}^{2} \times 3[/tex]

[tex] \frac{150.72}{3} [/tex]

=50.24 ft³

The cone formula is V=1/3(pi*r^2)h, plug in what you know 150pi=1/3(pi*r^2)8.

Multiply both sides by 3: 450pi=(pi*r^2)8

Divide by 8: 56.25pi=pi*r^2

Divide by pi: 56.25=r^2

Square root both sides: 7.5=r

Multiply by 2 to find diameter: d=15

Answer:

5/16 yd[tex]^{2}[/tex]

Answer:

B

Step-by-step explanation:

h(t) = t+3

Find h(1)

h(1) = 1+3

h(1) = 4

The answer is 4.

Answer:

Parallelogram are quadrilaterals with opposite sides parallel, but adjacent sides not perpendicular. If the sides have equal lengths, then it is called a rhombus.

Step-by-step explanation:

Because the sides of the shape meet at angles which are not 90 degrees, so they cannot be perpendicular.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

A shape can have parallel sides but not perpendicular sides if it is not a rectangle or a square. Examples of such shapes include parallelograms, trapezoids, and rhombuses. In these shapes, the sides are parallel to each other, but they are not perpendicular to each other.

Because the sides of the shape meet at angles which are not 90 degrees, so they cannot be perpendicular.

To learn more about parallel lines visit:

https://brainly.com/question/16701300.

#SPJ2