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Answer: 102

Step-by-step explanation:

Let the numbers be a, a+2 and a+4. Since the sum of three consecutive even numbers is 312, this will be:

a + a+2 + a+4 = 312

3a + 6 = 312

3a = 312 - 6

3a = 306

a= 306/3

a = 102

Therefore, the smallest number is 102.

Other numbers are 104 and 106.

Answer:

2( 4+4) = 16

Step-by-step explanation:

The gcf of 16+32 is 16

Answer:

The 99% confidence interval for the true average speed of a thunderstorm in his area is between 13.56 miles per hour and 16.44 miles per hour.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 13 - 1 = 12

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 12 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 3.0545

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.0545\frac{1.7}{\sqrt{13}} = 1.44[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 15 - 1.44 = 13.56 miles per hour

The upper end of the interval is the sample mean added to M. So it is 15 + 1.44 = 16.44 miles per hour.

The 99% confidence interval for the true average speed of a thunderstorm in his area is between 13.56 miles per hour and 16.44 miles per hour.

Answer:

6 x 2 x 3 = 36

Step-by-step explanation:

C is answer :)

Answer:

lets look at the width and the height and the length!

your width is: 6

your height is: 2

your length is: 3

Now lets multiply all given lengths to find the volume!

6 x 2 x 3 = 36 cubic inches!

Answer:

x = 55

Step-by-step explanation:

Since the sides of the shape are parallel, AngleC and AngleD will add up to 180° (see "parallel lines cut by a transversal" or maybe you have learned a big pile of parallelogram theorems)

Use this relationship to set up an equation.

2x + 20 + 50 = 180

combine like terms

2x + 70 = 180

subtract 70

2x = 110

divide by 2

x = 110/2

x = 55

x is 55

Answer:

The value of x is 55°

Step-by-step explanation:

Since we know that opposite angles of a parallelogram are equal

The sum of any two adjacent angles is supplementary. This means, ∠A + ∠B = 180°, ∠B + ∠C = 180°, ∠C + ∠D = 180°, and ∠D + ∠A = 180.

So,

∠C + ∠D = 180°

(2x + 20)° + 50° = 180°

2x + 70° = 180°

2x + 70° - 70° = 180° - 70°

2x = 110°

2x/2 = 110°

x = 55°

Thus, The value of x is 55°

Answer:

140

Step-by-step explanation:

7/.05 -140

Answer:

x^2 - 10x + 21

Step-by-step explanation:

Sum of zeros

= 7 + 3

= 10

Product of zeros

= 7 x 3

= 21

x^2 - ( sum of zeros )x + product of zeros

= x^2 - 10x + 21

The Quadratic polynomial is x^2 - 10x + 21.

if the zeroes of a quadratic polynomial are a and b, then the polynomial can be written as :

[tex] \boxed{{x}^{2} - (a + b)x + ab}[/tex]

So,

[tex] \hookrightarrow \: {x}^{2} - (7 + 3)x + (7 \times 3)[/tex]

[tex]\hookrightarrow \: {x}^{2} - 10x + 21[/tex]

12. The area of the shaded portion is the sum of the areas of a trapezoid and a parallelogram.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.

9. The area of the shaded region is the area of the smaller trapezoid subtracted from the area of the larger trapezoid which is,

= [{(1/2)×(10 + 6)×8} - {(1/2)×(5 + 3)×4}].

= [8×8 - 4×4] cm².

= 64 - 16 cm².

= 48 cm².

10. Similarly the figure in (10) is twice the area of the two trapezoids.

11. We have subtract the sum of the areas of the trapezoid and the triangle from the larger rectangle.

12. The total area is the sum of the areas of the trapezoid and the parallelogram.

13. The larger figure is a rectangle with a right-angle triangle on top.

We have to subtract two rectangles from this to obtain the area of the shaded region.

14. To obtain the area of the shaded region we have to subtract the area of the trapezoid from the larger triangle with a height of 10cm.

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Answer:

.38 or 38%

Step-by-step explanation:

I divided 44 by 116 then rounded

Answer: 38% of boys play an instrument.

Step-by-step explanation:

They are asking for the percentage of boys that play an instrument.

44 ÷ 116 = 0.379310...

Round to the nearest hundredth

0.38

Find the percentage

0.38 × 100 = 38 or 38%

Answer: it’s 161.50

Answer:

16/81

Step-by-step explanation:

Same as (2/3)^4

Answer:

$287.82

Step-by-step explanation:

60 * 2.30 = 138

30 * 2.75 = 82.5

34 * 1.98 = 67.32

138 + 82.5 + 67.32 = 287.82

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x)

[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]

from the graphs n f (x) and g( x) are 1 and 5 .

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Answer:

-729

Step-by-step explanation:

sequence is to multiply by -3 to get next term

Answer:

if it’s asking for a numerical answer it would be 1.67

(Rounded to the nearest two)

Step-by-step explanation:

Answer:

62

Step-by-step explanation:

Substitute x by 3 and y by 2

3*3*3*2+8=62

The cost function is a function that describes the total cost of producing x number of books. The fixed cost of 25000 is a constant cost that does not depend on the number of books produced, so it is not included in the cost function. The cost function is therefore:

Cost function: C(x) = 30x

The profit function is a function that describes the profit made from selling x number of books. The profit is equal to the revenue from selling the books minus the cost of producing the books. The revenue from selling x number of books at a price of 50 each is 50x, so the profit function is:

Profit function: P(x) = 50x - 30x = 20x

This profit function tells you that for every book you sell, you will make a profit of 20.

Answer:2024

Step-by-step explanation: 44x46

Answer:

6x + y = -8

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

m = -6

So

[tex]y = -6x + b[/tex]

(-2, 4)

This means that when [tex]x = -2, y = 4[/tex]. We use this to find b.

[tex]y = -6x + b[/tex]

[tex]4 = -6(-2) + b[/tex]

[tex]b = 4 - 12 = -8[/tex]

So

[tex]y = -6x + -8[/tex]

[tex]6x + y = -8[/tex]

Answer:

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

Given equation:

Its solutions are:

The product of the solutions is -15:

Answer:

cos 52 = 11/alpha ---> alpha = 11/cos52 = 17.9

Using division operation, since Benjamin jogs at a pace of 16 minutes per mile, in 45 minutes he will jog 2.8 miles.

The division operation is one of the basic mathematical operations, including addition, subtraction, and multiplication.

The division operation involves dividing the dividend (the numerator) by the divisor (the denominator) to obtain the quotient (the result).

The distance between Benjamin and Felix = 35 miles

Benjamin's jogging pace or speed = 16 minutes per mile

Felix's jogging pace or speed = 10 minutes per mile

The number of miles that Benjamin can jog in 45 minutes = Time/Speed

= 2.8125 miles (45/16)

Thus, Benjamin will jog 2.8 miles in 45 minutes.

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Answer:

The first statement and the 3rd statement are true. :)

For future reference, cosine is ratio of the adjacent side to the hypotenuse

Answer:

equation: 43+(-12x-9)+24x=X

Step-by-step explanation:

Answer:

y=1x-6

Step-by-step explanation:

First we find the slope by using rise over run. So you can either count up and over(rise/run) or use the slope formula y2-y1/x2-x1. You will find that the slope is 1, so plug that into the equation for mx. So we have y=1x so far. Then we find the y-intercept by looking where the graph intersects the y-axis. As you can see it intersects at -6, so plug -6 into the equation for b. No we have our full equation of y=1x-6.

-Hope this helped

Step-by-step explanation:

cross multiply

12-m(3m)= 1

12-3m²-1=0

multiply by -1

3m²+1-12=0

3m²= 11

m²= 11/3

m=√11/3.

Answer:

A

Step-by-step explanation:

refer the sketch for step by step answer