Easy
5
If 3x + 5y = 15 and x – 2y = 10, what is the value of 2x
+7y?

According to the information, the missing number from the box is number 40.

To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.

According to the above we can infer that the missing number is 40.

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Answer:

for question 13

Step-by-step explanation:

for 14

    x. 150

    y. 15

    z. 150

i cant say that this is totally correct but im taking a educated guess

Answer:

...

Step-by-step explanation:

The probability that exactly 29 out of 122 eligible voters aged​ 18-24 voted is approximately 0.282, or 28.2%.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

In this problem, we can use a normal approximation to the binomial distribution, since n=122 is large and the success probability p=0.22 is not too close to 0 or 1.

First, we need to calculate the mean and standard deviation of the binomial distribution:

mean = n * p = 122 * 0.22 = 26.84

standard deviation = sqrt(n * p * (1-p)) = sqrt(122 * 0.22 * 0.78) = 3.72

Next, we need to standardize the value of 29 to a standard normal variable:

z = (29 - 26.84) / 3.72 = 0.58

Finally, we can use a standard normal table or calculator to find the probability:

P(X = 29) = P(0.58 < Z < 0.58) = 0.282

Therefore, the probability that exactly 29 out of 122 eligible voters aged​ 18-24 voted is approximately 0.282, or 28.2%.

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The constant of proportionality is equal to 3/10.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/10 = 6/20 = 9/30

Constant of proportionality, k = 3/10.

Therefore, the required linear equation is given by;

y = kx

y = 3/10(x)

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Answer:

The width of the rectangle is 32cm and the length is 37cm.

Step-by-step explanation:

Answer:

A) PB M(b, m), we have;

b = 1

b = 2

b = 3

B) E(B) = 1.7

C) No they are not independent

Step-by-step explanation:

A) We are told that a shipment can be in 1 box for a small order, 2 boxes for a medium order, 3 boxes for a large order. Thus;

For PB M(b, m), we have;

b = 1

b = 2

b = 3

B) Factory Q is 60 miles from the company. Thus, under factory Q in the table, m = 60

Factory R is 180 miles from the company. Thus under factory R in the table, m = 180

Now;

P_B (b) for b = 1 which is small order is;

P_B (b) = 0.3 + 0.2 = 0.5

P_B (b) for b = 2 which is medium order is;

P_B (b) = 0.1 + 0.2 = 0.3

P_B (b) for b = 3 which is large order is;

P_B (b) = 0.1 + 0.1 = 0.2

Thus;

E(B) = Σb•P_B (b) = (1 × 0.5) + (2 × 0.3) + (3 × 0.2)

E(B) = 0.5 + 0.6 + 0.6

E(B) = 1.7

C) No, they are not independent. This is because from the table we are given, P_B,M at b = 1 and m = 60 is given as 0.3.

Whereas, for B and M to be independent, P_B,M at b = 1 and m = 60 has to be equal to (P_M(m) under m = 0.3) multiplied by P_B(b) for b = 1.

Instead what we have is P_M(m) under m = 0.3 as; 0.3 + 0.1 + 0.1 = 0.5. Which means (P_M(m) under m = 0.3) multiplied by P_B(b) for b = 1 gives;

0.5 × 0.5 = 0.25 which is not equal to P_B,M = 0.3 at b = 1 and m = 60

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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The total profit that the company would make on the trip can be found to be £7,320

The revenue that the company makes would be:

= Number of passengers x Amount that each passenger pays

= 400 x 23

= £9, 200

Each coach takes 50 passengers so the number of coaches needed are:

= 400 passengers / 50 passengers per coach

= 8 coaches

The total cost to the company for the trip is:
= (Number of coaches x Driver cost per coach) + (Number of coaches x Fuel per mile x Distance traveled for each coach)

= ( 8 x 95) + ( 8 x 70p x 200)

= 760 + 112, 000 p

= 760 + 112, 000/ 100 pence per pound

= £ 1,880

The total profit is:

= Revenue - total cost

= 9, 200 - 1, 880

= £7,320

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Answer:

x=14 x 7=98

Step-by-step explanation:

Answer:

the answer is X=98

Step-by-step explanation:

Answer:

\(x=30\\y=68\\z=82\)

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

\(y+z=5x\)

The third angle is 14 more than the second

\(z=y+14\)

And remember that the sum of these three angles must be equal to 180.

\(x+y+z=180\)

Let's take these equations

\(y+z=5x\\z=y+14\\x+y+z=180\)

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

\(x+y+z=180\\x+(y+z)=180\\x+(5x)=180\)

Distribute the + sign

\(x+5x=180\)

Combine like terms;

\(6x=180\)

Divide by 6.

\(x=\frac{180}{6}\\ x=30\)

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example \(z=y+14\)

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

\(x+y+z=180\\30+y+(y+14)=180\)

Distribute the + sign and Combine like terms;

\(30+y+y+14=180\\44+2y=180\\\)

Subtract 44 to isolate 2y.

\(2y=180-44\\2y=136\)

Now divide by 2.

\(y=\frac{136}{2}\\ y=68\)

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

\(x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82\)

Answer:

30+11x−28x2

Step-by-step explanation:

it is 30+11x-28x2

Answer:

\(g(x)=|x+2|+1\)

Step-by-step explanation:

Graph of a Modulus function:

Therefore, the parent function is:

\(\boxed{f(x)=|x|}\)

(Shown in red on the given graph).

From inspection of the given graph, the blue graph is the translated function.  As the left and right parts of the translated function are parallel to the left and right parts of the parent function, the graph has not been stretched and has only be translated (shifted).

To find the translation, study the vertex of both functions.  The vertex has been translated 2 units left and 1 unit up.

Translations

\(\textsf{For $a > 0$}:\)

\(f(x+a) \implies f(x) \: \textsf{translated $a$ units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated $a$ units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated $a$ units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated $a$ units down}\)

Therefore, the equation for the translated function is:

\(f(x+2)+1 \implies \boxed{ g(x)=|x+2|+1}\)

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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A line segment that measures 92 millimeters in length can be drawn using scale.

Given that,

A line segment has to be drawn which has a measure of length 92 millimeters.

We know that,

10 millimeters = 1 centimeter

1 millimeter = 1/10 centimeters

92 millimeters = 92/10 = 9.2 centimeters

So it is enough to draw a line segment of length 9.2 centimeters.

In the scale, between a centimeter, there are 9 small lines which indicates the millimeters.

In between 9 and 10, there are 9 lines which indicates, 9.1, 9.2, 9.3, ....., 9.9 and after that is 10 cm.

So draw a line segment starting from 0 to 9.2.

Hence the line segment is drawn with scale.

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The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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Answer:

Step-by-step explanation:

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Using linear function you would need to cross the bridge 30 times for the costs of the two toll options to be the same.

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Answer:

B. principal

Step-by-step explanation:

Answer:

4:7

Edit: I just saw the multiple choice options, in this case the right answer is:

but they're both equal

Step-by-step explanation:

The ratio you are looking for is

freestyle laps : (freestyle + butterfly) laps

so:

8 : (6+8)

8:14

Divide by 2 to simplify

4:7

The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:

6) 6\(\sqrt{2}\)

9) 40

10) \(\frac{5\sqrt{2} }{2}\)

11) 13

Step-by-step explanation:

6)A right triangle rule: if 2 legs are equal, the hypotenuse is the length of that leg*\(\sqrt{2}\)

9) Pythagorean Theorem

\(a^{2} +b^{2} =c^{2}\)

We know the hypotenuse (41) so we substitute that for c and 9 for b now we need to find a

\(\sqrt{41^{2}-9^{2} }\) which gives us 40

10) same with #6 but we do the opposite. SInce we have the hypotenuse, we can divide that by \(\sqrt{2}\) because we know that if 2 legs are equal, the hypotenuse is multiplied by \(\sqrt{2}\). Multiply the numerator and denominator by \(\sqrt{2}\) because we can't have a square root in the denominator.

11) like #9 we have the a and b but we need to find c

a=5 b=12 c=r

so \(\sqrt{5^{2}+12^{2} }\) which gives us 13

\( {h}^{2} = {p}^{2} + {b}^{2} \)

\( {c}^{2} = {6}^{2} + {6}^{2} \\ {c}^{2} = 36 + 36 \\ c = \sqrt{2( {6}^{2} )} \\ c = \sqrt{2}{\sqrt{ {6}^{{2}} } } \\ c = 6 \sqrt{2} \: \: \: ans\)

SOLUTION->

\( {h}^{2} = {p}^{2} + {b}^{2} \)

\( {41}^{2} = {x}^{2} + {9}^{2} \\ 1681 = {x}^{2} + 81 \\ 1681 - 81 = {x}^{2} \\ 1600 = {x}^{2} \\ x = \sqrt{40 \times 40} \\ x = 40 \: \: \: ans\)

GIVEN

\({h}^{2} = {p}^{2} + {b}^{2} \)

\( {5}^{2} = {s}^{2} + {s}^{2} \\ 25 = 2 {s}^{2} \\ 12.5 = {s}^{2} \\ \sqrt{12.5} = s \\ 3.5 = s \: \: \: ans\)

\( {h}^{2} = {p}^{2} + {b}^{2} \)

\( {r}^{2} = {12}^{2} + {5}^{2} \\ {r}^{2} \\ 144 + 25 \\ {r}^{2} = 169 \\ r = \sqrt{13 \times 13} \\ r = 13 \: \: \: \: ans\)

HOPE IT HELPED

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The equation of the line is y = x + 6

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

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 6

This means that the intercept c is 6

Also, as x changes by 1, the y values changes by 1

This mean sthat the slope is 1

So, we have

y = mx + c

This gives

y = x + 6

Hence, the equation is y = x + 6

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The linear equation on the graph can be written as:

y = (3/2)*x + 6

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁), then the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we can see the points (0, 6)  (so the y-intercept is b = 6)  and (4, 10)

Then the slope will be:

a = (10 - 6)/(4 - 0) = 6/4 = 3/2

Then the linaer equation is:

y = (3/2)*x + 6

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Answer:

The answer is Y+20> -30

Step-by-step explanation:

I took the test

The slopes of two parallel lines are the same, while the slopes of two perpendicular lines are the opposite reciprocals of each other. Each line has infinitely many lines that are parallel to it and infinitely many lines that are perpendicular to it.

P.S hopes this helps

Answer:

  5.2 square units

Step-by-step explanation:

You want the area of a triangle with sides 4 and 3, and the angle between them measuring 60°.

The formula for the area of a triangle is ...

  A = 1/2ab·sin(C)

Here, we have a=4, b=3, C=60°, so the area is ...

  A = 1/2·4·3·sin(60°) = 3√3 ≈ 5.2 . . . . square units

The area of the triangle is about 5.2 square units.

Answer:

1 1/5

Step-by-step explanation:

i took the k12 test