1 . 10. A life insurance company found that among its last 200 claims, there were six dozen smokers. What is the ratio of smokers to nonsmokers in this group of claimants? Write in lowest terms

2. A woman threw 60 darts and hit the target a dozen times. What is her ratio of hits to misses? Write in lowest terms

3. . While watching television for one week, a consumer group counted 1240 acts of violence and 40 acts of kindness. What is the violence to kindness ratio for television, according to this group. Write in lowest terms

The values of x and y in the similar triangles are 3 and 2 respectively.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, using similar triangle ratio, let's find the value of x and y.

x / 6 = 1.5 / 3

cross multiply

3x = 1.5 × 6

3x = 9

divide both sides by 3

x = 9 / 3

x = 3

Let's find y.

y / 4 = 1.5 / 3

cross multiply

3y = 6

divide both sides by 3

y = 6 / 3

y = 2

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The ratio of the combined volume of these pyramids to the volume of the prism as a fraction is equal to 1/3.

How to calculate the volume of a pyramid?

The volume of a pyramid can be calculated by using this formula:

Volume = 1/3 × b × h

Where:

h is the height.

b is the base area.

Here, both pyramids have the same base area as the prism, their volume is given by:

Volume of a pyramid = (1/3 × b × h) + (1/3 × b × h)

Volume of a pyramid = 2/3 × b × h

Also, the volume of this prism = 1/2 × b × h

Thus, the ratio is given by:

Ratio = (2/3 × b × h)/(1/2 × b × h)

Ratio = 2/3 × 1/2

Ratio = 1/3.

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Answer:

Triangular prism

Step-by-step explanation:

If you were to fold all the creases and glue it together you would get a tent shape which is a triangular prism

Answer:the quadratic function in f(x)= a(x-h)^2+k is f(x) = - (x - 2)² + 2.I think this is false";}

Step-by-step explanation:

well, there's no great mystery when it comes to getting a product from decimals.  Now, we have 611.2 and 0.0061, let's for a second take off the decimal point and simply multipy 6112 times 00061

6112 * 00061 = 372832

ok....... hmmm now let's see 611.2 had 1 decimal, whilst 0.0061 had hmm 4 decimals, let's add them up, that's 1 + 4 = 5 decimals total from both amounts, that simply means that our 372832 needs to have 5 decimals as well, so that makes it 3.72832.

Answer:

Step-by-step explanation:

the answer is 86

hope it helps!

(-_-)

Answer:

[tex]p+p+2=20[/tex]

Step-by-step explanation:

This is what my math teacher told us, so I don't know try this.

Step-by-step explanation:

p + j = 20

j = 2p + 2 --> -2p + j = 2

[tex] \binom{1 \: 1}{ - 2 \: 1} \: \binom{20}{2} = \binom{p}{j} [/tex]

1.because sample is random and (130)

(0.923) and (130)(0.077) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.923 and q=1-0.923=0.077

np = 130 x 0.923

np = 120 ≥ 10

nq = 130 × 0.077

nq = 10 = 10

Hence, Yes, because sample is random and

(130)(0.923) and (130)(0.077) are both at least 10. This means the normal model is a good fit for the sampling distribution.

2.because sample is random and (130)

(0.919) and (130)(0.081) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.919 and q=1-0.919=0.081

np = 130 x 0.919

np = 119.5 ≥ 10

nq = 130 × 0.081

nq = 10.5 ≥ 10

Hence, Yes, because sample is random and

(130)(0.919) and (130)(0.081) are both at least 10. This means the normal model is a good fit for the sampling distribution.

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Answer:

Step-by-step explanation:

a) 100cm 1m so, 320/100=3.2m, 1200/100=12m

b) 3.2+3.2+12+12= 6.4+24=30.4

c) 3*12=36m squared

d) 3.2*12= 3*12+0.2*12=36+2.4=38.4m squared

e) My estimate in d) was reasonable

f) This is because 36 and 38.4 are really close to each other they only have a difference of 2.4 and that is because instead of multiplying the estimate with 3 and a 0.2 I just multiplied it with a 3. 0.2*12=2.4 so the difference is reasonable.

The slope-Intercept form of the given line is y=x-1.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The given line passes through (0,-1) and (1,0). Therefore, the slope of the given line can be written as,

Slope of the line, m = [0 - (-1)]/(1 - 0)

                                 = 1 / 1

                                 = 1

Now, the equation of the line passing through (0,-1) can be written as,

y = mx + c

(-1) = 1(0) + C

-1 = 0 + C

C = -1

Substitute all the value in the equation of the line,

y = m(x) + c

y = 1(x) + -1

y = x - 1

Hence, the equation of the given line is y=x-1.

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The equation of the line from the given graph can be written as  y = x + 1.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

From the given graph the points on the straight line can be determined as (1, 0) and (2, 1).

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is given as slope = (y₂ - y₁) / (x₂ - x₁).

Then, the slope of the line is (2 - 1) / (1 - 0) = 1

Now, the equation of the line can be written as,

(y - 1) / (x - 0) = 1

⇒ y - 1 = x

⇒ y = x + 1

Hence, the equation of the line in slope-intercept form is given as y = x + 1.

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The solution of the equation given as -13x + x = 8x - 20x is infinite many solutions

From the question, the equation is given as

-13x + x = 8x - 20x

To start with, we need to rewrite the expression

So, we have the following representation

x - 13x = 8x - 20x

Solving further, we need to evaluate the like terms

So, we have the following equation

-12x = 8x - 20x

Evaluate the like terms again

So, the equation becomes

-12x = -12x

Both sides of the above equation are the same

i.e. -12x is on both sides of the equation

When we have a solution that all sides of the equation have the same value, then the solution is that the equation has infinite many solutions

Hence, -13x + x = 8x - 20x has infinite solutions

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Eli will take 12 hours alone to complete the task.

Acc to our question-

Hence,Eli will take 4 hrs.

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Answer: 31

Step-by-step explanation:

the prime factorization of 961 is 31×31  the value of the square root of 961 is 31.

Hope this helps! Have a good day! :)

Answer: Y=mx+b

Step-by-step explanation:

If you use the formula you can figure it out.

Answer:

the slope is 10

The slope represents the cost of gym membership per month.

Answer:

Step-by-step explanation:

Given:

Binomial: x² + 10x

To Find:

Solution:

To find the constant we would compare the binomial with (a + b)² i.e. a² + 2ab + b² as it is the formula for perfect square.

By comparing we get:

a² = x²

2ab = 10x

b² = constant (To find out)

From this we can make out:

a = x

[tex] \therefore[/tex]

[tex] \rm \implies 2 \times x \times b = 10x \\ \\ \rm \implies b = \frac{10x}{2x} \\ \\ \rm \implies b = 5 \\ \\ \therefore \\ \\ \rm \implies {b}^{2} = 25[/tex]

So, constant that should be added to the binomial so that it becomes a perfect square trinomial is [tex] \boxed{\rm 25} [/tex].

Perfect square trinomial is x² + 10x + 25

Factorisation of the trinomial:

[tex] \rm \implies {x}^{2} + 10x + 25 \\ \\ \rm \implies {x}^{2} + 10x + {5}^{2} \\ \\ \rm \implies {x}^{2} + 5x + 5x + {5}^{2} \\ \\ \rm \implies x(x + 5) + 5(x + 5) \\ \\ \rm \implies (x + 5)(x + 5) \\ \\ \rm \implies {(x + 5)}^{2} [/tex]

The dimension of the rectangle of the largest area in an equilateral triangle is √3/4L.

Here we have to find the dimension of the rectangle of the largest area.

Let the distance from the tip of the base of the triangle to the point that the top of the rectangle meets the triangle be x.

The width of the rectangle is √3/2 x.

By this, we can find the area of the rectangle

Area = √3/2x ( L -x) = √3/2 xL - √3/2x²

To find the maximum area we have:

dA/ dx = 0

dA / dx = √3/2L - √3x = 0

From we have to find the value of x,

√3 x = √3/2L

x = L/2

The dimension of rectangle is √3/2x = √3/2(L/2)

                                                             = √3/4 L

Therefore the dimension of the rectangle is √3/4 L.

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Answer:

Length YZ is about 16.2 cm (to the first decimal place)

Step-by-step explanation:

In order to find the lenth YZ we need to know the the Pythagorean theorem which is a²+b²=c² (or leg² + leg² = hypothnose)

For this problem let a = line segment XY, let b = YZ and let your hypothnose (c) to be ZX

Answer:

1) ∠5 and ∠6 are supplementary angles not vertical angles this statement is false.

2) ∠2 and ∠7 are alternally interior angles yeah that statement is true.

3) ∠2 and ∠4 are supplementary angles no they are not complementary, because sum of those two angles i.e. ∠2+∠4 =180.

so this statement is false

Step-by-step explanation:

Step-by-step explanation:

here ∠2+∠5=180°; ∠1+∠6=180; ∠4+∠7=180°; and for ∠3+∠7=180°;

here ∠6+∠8=180°; ∠1+∠3=180°; ∠2+∠4=180°; ∠5+∠7=180; here the

∠1=∠4; ∠2=∠3; ∠5=∠8; ∠6=∠7 (opposite angles are equal)

Using a proportional relationship, it is found that:

A. The slope of the line is of 4.

B. The slope is the same over both segments.

A proportional relationship is modeled as follows:

y = kx.

Hence a proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.

For the presented case, the two variables x and y are direct proportional, and thus the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k.

In this problem, the relationship has two points presented as follows:

(3, 12) and (4, 16).

Hence the slope, which is the constant of the relation, is given as follows:

k = 12/3 = 16/4 = 4.

Given two points, the slope is given by the change in y divided by the change in x. Hence, over each segment, the slopes are given as follows:

Which are the same slopes.

The problem is given by the image at the end of the answer.

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Answer:

x = 7

Step-by-step explanation:

Given equation,

→ 3x - 1 = 20

Now the value of x will be,

→ 3x - 1 = 20

→ 3x = 20 + 1

→ x = 21/3

→ [ x = 7 ]

Hence, the value of x is 7.

Answer: n=895

Step-by-step explanation:

Answer:

n = 895

Step-by-step explanation:

Here we want to find n , 1st form the Equation then solve it for n

0.1 times n = 0.1n

0.1 times n equal 89.5

Then 0.1n = 89.5

Solve for n , b dividing both sides by 0.1

n = 89.5 / 0.1 = 895

The coordinate geometry, the midsegment theorem shows that the midsegment of a triangle is 1/4 area of the triangle.

How to show that the midsegment of a triangle is 1/4 area?

The midsegment if a triangle is defined as a line that joins two midpoints of two opposite sides of a triangle.

The midsegment theory of a triangle states that in a triangle, the midsegments of 2 sides is parallel to, and half the length of the 3rd side.

The 3 midsegments of a triangle forms a small triangle within the larger triangle.

This therefore, forms 4 triangles.

Area of a triangle =base x height

Hence 4 triangles are formed,

The area of the larger triangle is [tex]\frac{bh}{4}[/tex] =1/4(bh)

Therefore;  Area =1/4 of area.

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Answer:

(y+12)/5=x

Step-by-step explanation:

y=5x-12

get x by itself

y+12=5x

divide both sides by 5

(y+12)/5=x

The distance when the mass is 5kg is 15cm.

When two values vary directly, it means that both values move in the same direction. If one of the value increases, the other value increases and if one of the values decreases, the other value decreases.

The equation that is used to represent direct variation is:

d = km

Where:

The first step is to determine the value of k:

12 = 4k

k = 12 / 4

k = 3

d = 3 x 5 = 15cm

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The coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).

To get the coordinates of a point reflected on the x - axis, some important rules be considered here:

1. The x - coordinate of the reflected point is the same as the x - coordinate of the original point.

2. The y - coordinate of reflected point has opposite sign of y-coordinate of original point.

Example:

(1,9) when reflected on the x - axis it will be (1,-9).

Therefore the  coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).

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Answer:

triangle CBA is congruent to triangle CDA

The triangles are not congruent

The absolute value graph has its equation to be f(x) = |x - 3| + 5

The graph represents the given parameter

From the graph, we can see that the graph is an absolute value graph

An absolute value graph is represented as

f(x) = a|x - h| + k

Where h and k are the vertex of the graph

In this case, they are

h = 3 and k = 5

This is because the minimum point of the graph is (3, 5)

Substitute values for h and k in the form of the equation

So, we have the following representation

f(x) = a|x - 3| + 5

A point on the graph is (2, 6)

This gives

a|2 - 3| + 5 = 6

When the value of variable a is solved, we have

a = 1

So, the equation becomes

f(x) = 1 * |x - 3| + 5

Evaluate the products

f(x) = |x - 3| + 5

Hence, the equation of the graph is f(x) = |x - 3| + 5

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Answer:

Step-by-step explanation:

18% of 430 comes out to 77.4 total pictures taken. After rounding it to the nearest whole number because you cant take a fraction of a picture it would be 77 total pictures taken.