Graph the solution set to this inequality.
35 - 1175 + 9

Answer:   -60

Step-by-step explanation:

i just found it good luck

:)

Answer:

237

Step-by-step explanation:

This is a system of equations.

The theater sold 364 adult and child tickets, so a + c = 364

They made a total of $1930. Each adult ticket was $6 & child tickets were $4. The second equation is 6a + 4c = 1930.

Let's line them up

a  +  c = 364

6a + 4c = 1930

Since we need to solve for the number of adult tickets, we want to get rid of the c variable. I'm going to multiply the entire first equation by -4 to do this. The second equation stays the same. Now, I have:

-4a - 4c = -1456

6a + 4c = 1930            Add them together

----------------------

2a = 474                      Divide by 2 to solve for a

a = 237

There were 237 adult tickets sold

The problem of scheduling exams for the high school students can be solved by using graph theory. We can represent the overlap of students in the form of a graph where each teacher is a node and the edges represent the students who belong to both the teachers classes.

To ensure that no student has to take more than one exam each day, we need to find a coloring of the graph such that no two adjacent nodes have the same color. This is equivalent to scheduling exams such that no two exams on the same day have any common students.

Using a greedy approach, we may overcome this issue by starting with any node and assigning it a color.. We then recursively color the neighbors of the node with a different color and so on. This algorithm will always produce a valid coloring since we are guaranteed to find a valid color for every node, given that we have not run out of colors.

In this case, we have seven teachers so we need at least seven colors. However we can find a valid coloring with fewer colors, depending on the structure of the graph. This problem can also be extended to more general situations, where we have more than one exam per day or where we have more complex constraints on the scheduling of exams.

The answer is general as no additional data is given.

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:

See below ↓

Step-by-step explanation:

Let's find the x and y values.

Step 1 : Equate the y expressions.

Step 2 : Convert fractions in the equation to whole numbers.

Step 3 : Bring x terms to one side and constant terms to the other.

Step 4 : Solve for y by plugging the value of x into one of the given equations.

Answer:

197

Step-by-step explanation:

\(5 \times 5 \times 2 + 5 \times (5 + 9) \times \frac{1}{2} \times 2 + 5 \times 9 + 5 \times 6.4 = 197\)

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

A) a = 25

B) b = 14

Step-by-step explanation:

hopefully this helps :)

Solve the following:

\( \\ \sf \: a) \: \: \frac{a}{5} + 3 = 8\)

\( \\ \sf \: b) \: \: \frac{3b}{7} - 1 = 5\)

Solving question a) :

\( \\ \sf \frac{a}{5 } + 3 = 8\)

\( \\ \sf \mapsto \frac{a + 15}{5} = 8\)

\( \\ \sf \mapsto \: a + 15 = 8 \times 5\)

\( \\ \sf \mapsto \: a = 40 - 15\)

\( \\ \sf \mapsto \: a = 25\)

\( \\ \sf \therefore \: a = 25\)

Solving question b) :

\( \\ \sf \frac{3b}{7} - 1 = 5\)

\( \\ \sf \mapsto \: \frac{3b - 7}{7} = 5 \)

\( \\ \sf \mapsto3b - 7 = 5 \times 7\)

\( \\ \sf \mapsto3b = 35 + 7\)

\( \\ \sf \mapsto \: b = \frac{42}{3} \)

\( \\ \sf \mapsto \: b = 14\)

\( \\ \sf \therefore \: b = 14\)

a = 25

b = 14

The calculated value of the rate of the graph is 0.8

from the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

(0, -16) and (20, 0)

The rate of the graph is calculated as

Rate = Change in y/x

using the above as a guide, we have the following:

Rate = (0 + 16)/(20 - 0)

Evaluate

Rate = 0.8

Hence, the rate is 0.8

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Answer:

x = 15°

Step-by-step explanation:

(5x-15) + 75 + 3x = 180

8x + 60 = 180

8x = 120

x = 15°

Answer:

a)125/291

b) 48/73

Step-by-step explanation:

a) total of yes/total asked

b) total above average yes/ total above average (yes and no)

Answer:

See explanation. You didn't specify on whether the problem asks for a fraction or decimal, so I put both decimal and fraction.

Step-by-step explanation:

First we answer a:

Total amount of people polled is 291. Number of people who wear glasses is: \(48 + 51 + 26 = 125\)

Divide to get the proportion: \(\frac{125}{291}\) which is also equal to: 0.4295532646

Then we answer b:

b asks for the proportion of all above average readers who wear glasses, so the total number would be: \(48 + 25 = 73\). The number of above average readers who wear glasses is then 48.

We then get the proportion: \(\frac{48}{73}\), which is also equal to 0.6575342466.

The answer is A.

Since 4.5 is the first number, that is the starting point.

Since we are subtract 2.5, we are going to move 2.5 units to the left of 4.5.

Subtract to check.

4.5 - 2.5 = 2 (Final point is at 2)

The only number line that satisfies our needs is A. Thus, proves our answer.

Best of Luck!

Answer:

A

Step-by-step explanation:

Answer:

f(1)= 3(1-1)

f(1)=3×0

f(1)=0

Answer:

yes make the triangle 2/3 the size it is right now most likely by dragging it inwards

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

Answer:

1) y=-11x-50    2)y=-8x+16

Step-by-step explanation:

1.  y=mx+b- it is the main equation for a line'

If we take the first point and use its coordinates we have -6=-4m+b

If we take the second point and use its coordinates we have 5=5m+b

These equations are simultaneous for our line because the line passes through both points

-6=-4m+b

5=-5m+b

If subtract the second one from the first equation

-6-5= -4m+b- (-5m+b)

-11= m

b= -6-44=-50

y=-11x-50

2) y=mx+b

-8=-8*3+b

b=16

y=-8x+16

We want to calculate the volume of the spherical shell of chocolate.

The chocolate shell is spherical with a thickness of 0.5cm

Volumes of spherical shells can be calculated with the formula;

The outer diameter is 8cm. The outer radius is therefore 4cm

The inner diameter is 8-2(0.5)=7cm. The inner radius is therefore 3.5cm

Therefore, we can find the volume of the chocolate shell as;

Therefore,

Answer:

The null hypothesis is rejected.

There is enough evidence to support the claim that rates are higher for single male policyholders verses married male policyholders (P-value = 0.004).

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that rates are higher for single male policyholders verses married male policyholders.

Then, the null and alternative hypothesis are:

\(H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0\)

The significance level is 0.05.

The sample 1 (single group), of size n1=450 has a proportion of p1=0.1489.

\(p_1=X_1/n_1=67/450=0.1489\)

The sample 2 (married group), of size n2=925 has a proportion of p2=0.1005.

\(p_2=X_2/n_2=93/925=0.1005\)

The difference between proportions is (p1-p2)=0.0483.

\(p_d=p_1-p_2=0.1489-0.1005=0.0483\)

The pooled proportion, needed to calculate the standard error, is:

\(p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{67.005+93}{450+925}=\dfrac{160}{1375}=0.1164\)

The estimated standard error of the difference between means is computed using the formula:

\(s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.1164*0.8836}{450}+\dfrac{0.1164*0.8836}{925}}\\\\\\s_{p1-p2}=\sqrt{0.0002+0.0001}=\sqrt{0.0003}=0.0184\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.0483-0}{0.0184}=\dfrac{0.0483}{0.0184}=2.62\)

This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):

\(P-value=P(z>2.62)=0.004\)

As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that rates are higher for single male policyholders verses married male policyholders.

Answer:15x+35=110

Step-by-step explanation:

Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

Answer:

12

Step-by-step explanation:

The two unknown values of the triangle have to be the same.

Subtract 28 from 180 and you get 152

So each angle will be 76.

So now, 76 = -8 + 7x

Simplify and 84 = 7x

Now, x is equal to 12

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By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

The surface area of the sphere is 1810 cm²

A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of sphere is expressed as;

A = 4πr². where r is the radius.

A = 4 × 3.14 × 12²

A = 1809.7 cm²

approximately to the nearest whole number

A = 1810 cm²

Therefore the surface area of the sphere to the nearest whole number is 1810 cm².

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A is the answer to this question

Answer:

  Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

Step-by-step explanation:

Both expressions are linear expressions. It takes 2 points to define a line. If the lines defined by each expression go through the same two points, then the expressions are equivalent.

If the expressions have the same value for two different variable values, they are equivalent. (choice D)

_____

Additional comment

One more point is needed than the degree of the polynomial expression. That is, quadratic (degree 2) expressions will be equivalent if they go through the same 2+1 = 3 points.

Answer:

Step-by-step explanation:

9. sin 18 = x/21

 x = 21* sin 18

  x = 6.5

10. tan 55 = 29/x

  x* tan 55 = 29

x = 29/tan 55

x = 20.3

11. sin 23 = x/25

  x = 25 * sin 23

  x = 9.8

12. sin 47 = 33/x

  x * sin 47 = 33

 x = 33/sin 47

  x = 45.1

Answer:

  £930  

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic. The annual earnings are expected to be 12 times the monthly earnings.

  T = 0.2(12×£1375 -11850) = 0.2(£16500 -11850) = 0.2(£4650)

  T = £930

The caterer will pay £930 in income tax for the year.

Answer:

£930  

Step-by-step explanation:

         Monthly income = £1375

     y = Yearly income  = 12 × 1375 = £16 500

     p = Personal allowance            =    11 850

y - p = Taxable income                   = £ 4 650

    T = 0.2(y - p) = 0.2 × £4650       = £    930

The income tax for the year will be £930.

Answer:

-4

Step-by-step explanation:

Since they all have the same base;

Answer:

Slope intercept form with m= -7

Step-by-step explanation:

Slope intercept form is y=mx+b

where m=slope and b=y-intercept

so

y=-7x+2

Slope (m)= -7

y-intercept = 2