This table shows information about the number of
days of holiday taken last year by the employees at a
company.
Calculate the mean number of holiday days taken.
Give your answer to 1 d.p.
Holiday days taken 25
26
27
28
29
30
Frequency
6 9 7 7 3 0
2

Answer:

[tex]h^{-1}(x) = \frac{4}{3}x + \frac{23}{3}[/tex]

Step-by-step explanation:

Given

Graph h:

[tex](x_1,y_1) = (1,-5)[/tex]

[tex](x_2,y_2) = (9,1)[/tex]

Required

Plot [tex]h^{-1}(x)[/tex]

First, calculate h(x)

Calculate slope (m)

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

[tex]m = \frac{1--5}{9-1}[/tex]

[tex]m = \frac{6}{8}[/tex]

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

The equation is:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = \frac{3}{4}(x - 1) -5[/tex]

[tex]y = \frac{3}{4}x - \frac{3}{4} -5[/tex]

[tex]y = \frac{3}{4}x + \frac{-3 - 20}{4}[/tex]

[tex]y = \frac{3}{4}x - \frac{23}{4}[/tex]

Next, calculate [tex]h^{-1}(x)[/tex]

Swap y and x

[tex]x = \frac{3}{4}y - \frac{23}{4}[/tex]

Solve for y

[tex]\frac{3}{4}y = x + \frac{23}{4}[/tex]

Multiply through by 4

[tex]3y = 4x + 23[/tex]

Divide through by 3

[tex]y = \frac{4}{3}x + \frac{23}{3}[/tex]

Replace y with [tex]h^{-1}(x)[/tex]

[tex]h^{-1}(x) = \frac{4}{3}x + \frac{23}{3}[/tex]

See attachment for graph

Answer:

Step-by-step explanation:

1) x-y=18

2) 2x/7-y/4=6

from 1) x=18+y      substituting in 2)

2(18+y)/7-y/4=6

36/7+y(2/7-1/4)=6

y=(6-36/7)/(2/7-1/4)

y=(6/7)/(1/28)

y=24

x=18+y=18+24

x=42

Step-by-step explanation:

Given that,

BC = 8

Ac = 15

We can find AB using the pythagoas theorem.

[tex]AB=\sqrt{AC^2+BC^2}\\\\=\sqrt{15^2+8^2}\\\\AB=17[/tex]

We know that,

[tex]\cos\theta=\dfrac{B}{H}[/tex], B is base and H is Hypotenuse

[tex]\cosB=\dfrac{8}{17}[/tex]

Hence, this is the required solution.

Answer:

Thomas is 28.

Step-by-step explanation:

Let Huilan’s age be “x + 11”

Let Thomas’s age be “x”

x + x + 11 = 67

2x + 11 = 67

2x = 56

x = 28 years

x + 11 = 39 years

Thomas is 28.

Answer:

3 Pounds of Coffee

Step-by-step explanation:

To find out how much she spent on the pounds of coffee, you would have to takeaway $65.37 away from the total of $90 which will give you $24.63, which is how much she has spent on the coffee. To find out how many pounds of coffee she bought, you would have to divide $24.63 by $8.21 giving you 3, which is how many pounds of coffee Teresa bought.

Much appreciated if this is marked as brainliest :)

Answer:

A. 3.3%

Step-by-step explanation:

We use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses 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 zscore 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 pvalue, 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].

250 babies, boys and girls equally as likely:

This means that [tex]n = 250, p = 0.5[/tex].

Mean and standard deviation:

[tex]\mu = E(X) = np = 250*0.5 = 125[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.5*0.5}[/tex]

Probability that out of 250 babies born, 110 or fewer will be boys?

Using continuity correction, this is P(X < 110 + 0.5) = P(X < 110.5), which is the p-value of Z when X = 110.5. So

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

[tex]Z = \frac{110.5 - 125}{\sqrt{250*0.5*0.5}}[/tex]

[tex]Z = -1.83[/tex]

[tex]Z = -1.83[/tex] has a p-value of 0.033

0.033*100% = 3.3%, so option A.

Answer:

990

Step-by-step explanation:

99+88+77+66+55+44+33+22+11+11+22+33+44+55+66+77+88+99=990

Answer:

Answer:

990

Step-by-step explanation:

99+88+77+66+55+44+33+22+11+11+22+33+44+55+66+77+88+99=990

Step-by-step explanation:

Answer:

(x+7)^2+(y+9)^2=16

Step-by-step explanation:

This is the equation written in standard form, I'm not sure if that's what you wanted.

Answer:

∨∨∨∨see below∨∨∨∨∨∨

Step-by-step explanation:   6  26  18  13

The two outside angles are congruent.  The two inside angles are supplemental thus they are equal.  The last two angles the high one and the lower one must sum to 180° in their respective triangles so they are equal since their similar angles are equal.

find x

4 is to x as 5 is to 7.5

   4/x = 5/7.5      solve for x

   4 × 7.5 / 5  = x

    30 / 5  =  x

       6 = x

The six trigonometric function of [tex]\theta[/tex] are [tex]\sin \theta \approx 0.781[/tex], [tex]\cos \theta = - \frac{5}{8}[/tex], [tex]\tan \theta \approx -1.250[/tex], [tex]\cot \theta \approx -0.800[/tex], [tex]\sec \theta = - \frac{8}{5}[/tex], [tex]\csc \theta \approx 1.280[/tex], respectively.

In this question, we assume that x-component of the terminal point is part of a unit circle. Then, we can find the value of y by means of the Pythagorean theorem:

[tex]y = \sqrt{1-x^{2}}[/tex] (1)

If we know that [tex]x = -\frac{5}{8}[/tex] and P is in the second quadrant, then the value of y is:

[tex]y = + \sqrt{1-\left(-\frac{5}{8} \right)^{2}}[/tex]

[tex]y \approx 0.781[/tex]

By trigonometry, we remember the following definitions for the six basic trigonometric functions:

[tex]\sin \theta = \frac{y}{1}[/tex] (1)

[tex]\cos \theta = \frac{x}{1}[/tex] (2)

[tex]\tan \theta = \frac{y}{x}[/tex] (3)

[tex]\cot \theta = \frac{1}{\tan\theta}[/tex] (4)

[tex]\sec \theta = \frac{1}{\cos \theta }[/tex] (5)

[tex]\csc \theta = \frac{1}{\sin \theta}[/tex] (6)

If we know that [tex]x = -\frac{5}{8}[/tex] and [tex]y \approx 0.781[/tex], then the six basic trigonometric functions are, respectively:

[tex]\sin \theta \approx 0.781[/tex], [tex]\cos \theta = - \frac{5}{8}[/tex], [tex]\tan \theta \approx -1.250[/tex], [tex]\cot \theta \approx -0.800[/tex], [tex]\sec \theta = - \frac{8}{5}[/tex], [tex]\csc \theta \approx 1.280[/tex]

The six trigonometric function of [tex]\theta[/tex] are [tex]\sin \theta \approx 0.781[/tex], [tex]\cos \theta = - \frac{5}{8}[/tex], [tex]\tan \theta \approx -1.250[/tex], [tex]\cot \theta \approx -0.800[/tex], [tex]\sec \theta = - \frac{8}{5}[/tex], [tex]\csc \theta \approx 1.280[/tex], respectively.

We kindly invite you to check this question related to trigonometric functions: https://brainly.com/question/6904750

Answer:

Both the mean and median and they both gives a measure of 17

Step-by-step explanation:

Given the data about the ages of 7 people :

17,20,22,12,15,12,21

Ordered data: 12, 12, 15, 17, 20, 21, 22

To find the median :

Median = 1/2 * (n+1)th term

n = number of observations = 7

Median = 1/2(7+1)th term

Median = 1/2 *8 = 4th term = 17

Mean = Σx / n = (sum of ages) / number of observations

Mean = 119 / 7 = 17

:

Answer:

im sorry i took long im not the best at math but since 10 equals r im not sure what you need to know but i think its 3+5r=80 i hope this help

Step-by-step explanation:

Answer:

12,867.859375

Step-by-step explanation:

24.5/7 = 3.5

Geometric sequence

A_n = 7 * (3.5)^(n - 1)

A_7 = 7 * (3.5)^(7 - 1)

A_7 = 12,867.859375

Answer:

I put 6/9 even though i know its wrong

Step-by-step explanation:

Answer:

option c is the correct answer

first take y raised to the power 4 common then cancel its power by y raised to the power 3

you get your answer

Answer:

Similar to your other question. Now, you're looking for the score such that this time, 0.99 corresponds to a z-score of approximately, which means

Step-by-step explanation:

u have solve it by finding slope(m)

and substitute is general eq of straight line

y = mx + c

Answer:

y = 2x - 6

Step-by-step explanation:

These are actually pretty fun to do once you get the hang of it! Here are the steps!

The formula for slope intercept form is y=mx + b.

m is the slope and b is the y-intercept. Let's start with finding the y-intercept (also known as b).

To find the y-intercept, look at where the line crosses the y-axis. In your equation, the line crosses the y-axis at -6. Plug -6 in for b in the equation.

y = mx + (-6)

Now were going to find the slope. To find the slope, you need to find the rise over run. To start, first find a point on the graph where the line goes through an integer (just pick one of the blue dots). Then, count how many squares you go up or down, and how many you go to the left or right before you hit the next blue dot. Divide the rise over the run, and you have your slope! Here are the steps for the problem:

To get from one dot to another, you rise up 2 units, and you run to the right 1 unit. Plugging those integers into rise/run, you get 2/1 which simplifies to 2. That's your slope.

Now all we need to do is plug the slope into the formula, and you have your equation!

Answer: y = 2x - 6

Answer:

P(X < 1) = 0.5

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal 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.

Mean of 1 L and standard deviation of 0.05 L.

This means that [tex]\mu = 1, \sigma = 0.05[/tex]

Find P(X < 1).

This is the p-value of Z when X = 1. So

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

[tex]Z = \frac{1 - 1}{0.05}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5. Thus

P(X < 1) = 0.5

Answer:

MEDIA: 4.8

MEDIANA: 5

MODA: 5

espero que te ayude :)

Answer:

17.83 in

Step-by-step explanation:

2 x 3.14

= 6.28

112 ÷ 6.28= 17.8343949

Whole number is 17.83 in

Answer:

180 gallons of water

Step-by-step explanation:

4×6×1=24

24×7.5=180

Hope this helps!

Answer:

Base = 19

Height = 26

Step-by-step explanation:

Given :

Height, h = base, b + 7 feets

The area of triangle, A = 247 ft²

The area of a triangle is given by :

A = 1/2 * base * height

247 = 1/2 * b * (b + 7)

247 = 0.5 * b * (b + 7)

247 = 0.5b² + 3.5b

0.5b² + 3.5b - 247 = 0

Solving the quadratic equation ; using the quadratic equation solver, the roots are :

b = -26 or b = 19

Length of base can't be negative :

Hence,

Base, b = 19

Height, h = base + 7 = 19 + 7 = 26

Answer:

Option D

Step-by-step explanation:

Given f(x) = [tex]\sqrt[3]{4x}[/tex]

g(x) = 2x + 3

Since, [tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]

                     [tex]=\frac{\sqrt[3]{4x}}{2x+3}[/tex]

This function is defined for the denominator is not equal to zero.

(2x + 3) ≠ 0

x ≠ [tex]-\frac{3}{2}[/tex]

Therefore, Option D will be the correct option.

Answer:

b. He should use the two-sample test of the mean to answer question one and the two-sample test of proportion to answer question two.

Step-by-step explanation:

Here we have two independent groups, Men and Women, therefore, to show if it is the Men or Women who performed better, this can be determined based the mean scores of each group. Therefore, use the two sample test of mean which is used to test whether the unknown mean of two independent population are equal or not.

In other to determine those who have the greater number of admissions between the two groups, this is determined by comparing the proportion of each group admitted. Hence, rather Than testing for the mean, we compare the proportion. Hence, we use the two sample test of proportion.

Answer:

x+80=70°(exterior alternate angles)

x=70-80

x=-10

Answer:  each brace is 2 & 2/3 inches long

=====================================================

Explanation:

"he cuts 4 feet from a board that's 8 feet long" means that he has 8-4 = 4 feet to work with. This converts to 4*12 = 48 inches.

Next, we cut that into 18 equal pieces

48/18 = 8/3 = 2 & 2/3

This is approximately 2.667 inches

Answer:

B abd = cbe

Step-by-step explanation:

ABC = DBE

so

ABC + CBD = DBE + CBD

The statement which is true is ZABC - ZABD, the correct option is A.

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

We are given that;

Angle ABC = Angle DBE

Now,

A flowchart proof is a formal proof that is set up with boxes that flow from one to the next with arrows1. The statements, which are true facts that we know, are placed in the boxes, with the reason we know them on a line underneath2. We can prove theorems are true using flowchart proofs.

To justify each step in the flowchart proof, we have to provide a reason for each statement based on definitions, postulates, properties or previously proven theorems. Here is how we can fill in the blanks:

A: Given B: Definition of angle bisector C: Definition of congruent angles

Therefore, graphically the answer will be ZABC - ZABD.

Learn more about finding the solution graphically here:

https://brainly.com/question/26254258

#SPJ7

Answer:they have the same vertical stretch

Step-by-step explanation:

9514 1404 393

Answer:

  x + y = 6   (or choice C, see comment)

Step-by-step explanation:

The equation of the line through point B and perpendicular to AB can be written as ...

  (Bx -Ax)(x -Bx) +(By -Ay)(y -By) = 0 . . . . where A = (Ax, Ay) and B = (Bx, By)

  (2 -(-3))(x -2) +(4 -(-1))(y -4) = 0

  5x +5y -30 = 0

  x + y = 6 . . . . . . reduce to standard form

__

Additional comment

None of the offered choices describes a line through point B. (See second attachment). We note that several of the lines go through the point (4, 4). The segment joining points (-3, -1) and (4, 4) will be perpendicular to the line -7x -5y = -48, answer choice C.

Please talk to your teacher about this question.