​Choose the right answer.

Two hundred fifty tickets are sold at a fund raiser. If Sarah buys 15 tickets, the probability that she will win the prize quilt is
6%
7.5%
15%

Final answer:

To find the ratio that forms a proportion with 9/5, we can find a common multiplier for each option and check if the resulting ratios are equal to 9/5.

Explanation:

If we want to determine which ratio forms a proportion with 9/5, we can find a common multiplier. We can multiply both the numerator and denominator of each ratio by the same number and check if the resulting ratios are equal to 9/5.

Let's check each option:

Therefore, the ratio 54/30 (option a) forms a proportion with 9/5.

The given equation in slope-intercept form is y = -2x - 2.

Slope of a line is defined as the change in the value of y-coordinate with respect to the x-coordinate value. It is usually denoted by 'm'.

It can also be defined as the tangent of the angle that the given line is making with the X-axis.

That is m = tan θ, where θ is the angle that line is making with the X-axis.

The equation of a line in slope-intercept form is given by,

y = mx + c

Here, c is called the y-intercept, the value of which is the value of the y-coordinate when the line touches the Y-axis.

Now,

y + 4 = -2 (x - 1)

y + 4 = -2x + 2

y = -2x + 2 - 4

y = -2x - 2

The equation of the line in slope-intercept form is y = -2x - 2.

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The correct option that describes the volume of a cylinder is B: the area of the circular base multiplied by the height of the cylinder, represented by the formula \(V = \pi r^2 h\).

The volume of a cylinder is best described by option B, which states it is the area of the circular base multiplied by the height of the cylinder. The area of the base, which is a circle, is calculated using the formula \\(\pi r^2\), where \(r\) represents the radius of the circle. To find the volume, this area is then multiplied by the height \(h\) of the cylinder, giving the formula for the volume \(V = \pi r^2 h\).

Answer:

The area of the triangle is, [tex]56 cm^2[/tex]

Step-by-step explanation:

Area of the triangle(a) is given by:

[tex]a = \frac{1}{2} \cdot bh[/tex]           ....[1]

where,

b is the base and h is the height of the triangle.

As per the statement:

Given:

h = 8 cm

b = 14 cm

Substitute in [1] we have;

[tex]a = \frac{1}{2} \cdot 8 \cdot 14 = 4 \cdot 14[/tex]

⇒[tex]a = 56 cm^2[/tex]

Therefore, the area of the triangle is, [tex]56 cm^2[/tex]

By applying the concept of Least Common Multiple (LCM), which is 12 in this case, we realize that Eddie will perform all three activities on the same day again after 12 days and that the day will be a Friday.

If Eddie goes jogging every other day (2 days), lifts weights every third day (3 days), and swims every fourth day (4 days), then we must find the LCM of 2, 3, and 4 to find out when will he do all three activities on the same day again.

The LCM of 2, 3, and 4 is 12. Therefore, Eddie will perform all three activities on the same day after 12 days. If he begins on Monday, he will surprisingly end up on a Friday, as the 12th day falls on a Friday. This is because, typically, 7 days from Monday is another Monday. Therefore, five additional days (to total 12) will fall on a Friday.

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The answer is c.

F(x)=5x^3+7x^4-1/2x

The equation of the tangent line to the curve is derived by first finding the slope of the tangent line at a certain point using implicit differentiation. After finding the slope, we then use the point-slope form of a linear equation to get the equation of the tangent line.

To find an equation of the tangent line to the curve given by the equation xey + yex = 5, it's necessary to find the derivative of the function, which gives us the slope of the tangent line at any point. Implicit differentiation is the key here, since y is not explicitly solved in terms of x.

Differentiating the given equation implicitly with respect to x, we get: exy + yex +ex + yex = 0. From this, we can express dy/dx (the derivative of y with respect to x, i.e., the slope of the tangent line) in terms of x and y.

Next, simply plug in the given coordinates of the point at which we are finding the tangent into this dy/dx equation. This gives the slope of the tangent line at the specific point.

To finally find the equation of the tangent line, use the point-slope form of a linear equation y - y1 = m(x - x1), where m is the slope we found, and (x1, y1) are the coordinates of the point. Substitute these values in, and that gives the equation of the tangent line to the curve at the point.

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Answer:

First option is correct.

Step-by-step explanation:

In triangle ABC, [tex]\angle A=8x-2[/tex], [tex]\angle B=2x-8[/tex] and [tex]\angle C=94-4x[/tex].

According to angle sum property of a triangle, the sum of interior angles of a triangle is 180 degree.

[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]8x-2+2x-8+94-4x=180[/tex]

[tex]6x+84=180[/tex]

[tex]6x=96[/tex]

Divide both sides by 6.

[tex]x=16[/tex]

Therefore the value of x is 16. The measure of angles are

[tex]\angle A=8(16)-2=126[/tex]

[tex]\angle B=2(16)-8=24[/tex]

[tex]\angle C=94-4(16)=30[/tex]

The opposite angle of shortest side is always smallest interior angle. Similarly the opposite angle of longest side is always largest interior angle.

[tex]\angle B<\angle C<\angle A[/tex]

[tex]AC<AB<BC[/tex]

Therefore option 1 is correct.

Answer:

x = -2

Step-by-step explanation:

Answer:

[tex]g(f(x))=-9x^2[/tex]

Step-by-step explanation:

[tex]f(x) = -3x^2[/tex]

[tex]g(x) = 3x[/tex]

WE need to find composition of function g(f(x))

To find g(f(x)) we replace f(x) in g(x)

[tex]g(f(x))= g(-3x^2)[/tex]

Now we replace -3x^2 inside g(x)

[tex]g(-3x^2)=3(-3x^2)= -9x^2[/tex]

[tex]g(f(x))=-9x^2[/tex]

Answer:

C) circle

Step-by-step explanation:

In order to write [tex]\frac{18}{25}[/tex] as a decimal, we need to find a fraction equivalent to[tex]\frac{18}{25}[/tex] with a 100 in the denominator. Notice that if we multiply the numerator and the denominator of [tex]\frac{18}{25}[/tex] by 4, we get the equivalent fraction [tex]\frac{72}{100}[/tex] which we can now write as a decimal. Remember that the hundredths place is 2 places to the right of the decimal point. Therefore, we can write [tex]\frac{72}{100}[/tex] as 0.72.

To write a fraction to a percent, first remember that a percent is a ratio of a number to 100 so to write [tex]\frac{18}{25}[/tex] as a percent, we need to find a fraction equivalent to [tex]\frac{18}{25}[/tex] that has a 100 in the denominator. We can . do this by setting up a proportion.

[tex]\frac{18}{25}[/tex] ≈ [tex]\frac{n}{100}[/tex]

Now, we can use cross products to find the missing value.

25n = 1800

÷ 25     ÷25

n = 72%

Therefore, [tex]\frac{18}{25}[/tex] is equal to 72%.

Aidan makes 8 bracelets each day from Tuesday to Thursday, resulting in 24 bracelets for those three days. Adding this to the 12 he made on Monday gives us 36 bracelets up to Thursday. Aidan continues the same pattern on Friday, making 8 more bracelets, totaling 44 bracelets.

To determine how many bracelets Aidan makes on Friday, we need to calculate the total number he makes from Tuesday through Thursday and then add it to the number of bracelets he already made on Monday. He starts with 12 bracelets on Monday and makes 8 more each day from Tuesday to Thursday. Calculating the bracelets made from Tuesday through Thursday involves multiplication of the daily bracelet count by the number of days.

Aidan makes 8 bracelets each day for three days, which is calculated as follows:

We then add this to the initial 12 bracelets made on Monday:

Since the pattern of bracelet making doesn’t specify any change on Friday, we assume Aidan continues to make 8 bracelets on Friday as well. So, he makes 8 bracelets on Friday.

The total number of bracelets Aidan makes up to Friday is the sum of bracelets made from Monday through Thursday plus the bracelets made on Friday:

Final answer:

Aidan makes 44 bracelets on Friday.

Explanation:

To find out how many bracelets Aidan makes on Friday, we need to calculate the total number of bracelets he makes from Monday through Thursday. On Monday, Aidan makes 12 bracelets. From Tuesday through Thursday, he makes 8 more bracelets each day. So the number of bracelets he makes on Tuesday is 12 + 8, on Wednesday is 12 + 8 + 8, and on Thursday is 12 + 8 + 8 + 8.

Now, to calculate the number of bracelets he makes on Friday, we need to add 8 to the total number of bracelets he made on Thursday. So the total number of bracelets he makes on Friday is 12 + 8 + 8 + 8 + 8.

Therefore, Aidan makes 12 + 8 + 8 + 8 + 8 = 44 bracelets on Friday.

Answer:

option (c) is correct,

[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

Step-by-step explanation:

Given expression ,  [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

We have to choose an equivalent fraction from the given options.

Consider expression (c) ,

[tex]3x^2+17-\frac{82}{x+5}[/tex]

Taking LCM , Multiply [tex]3x^2+17[/tex] by (x+5) , we get,

[tex]\frac{3x^2(x+5)+17(x+5)-82}{x+5}[/tex]

On solving , we get,

[tex]\frac{3x^3+15x^2+17x+85-82}{x+5}[/tex]

On simplifying, we get,

[tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

Which is equal to the given expression.

Thus, option (c) is correct,

[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

The solutions of the quadratic equation [tex]8m^2 + 20m = 12[/tex] by factoring method are [tex]m = \dfrac{1}{2}[/tex] and [tex]m = - 3[/tex]

Using the formula of the quadratic equation which states that,

The roots of the standard form of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] are calculated as,

[tex]x = \dfrac{- b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Given that,

A quadratic equation,

[tex]8m^2 + 20m = 12[/tex]

Now, simplify the equation,

[tex]8m^2 + 20m = 12[/tex]

Subtract 12 on both sides,

[tex]8m^2 + 20m - 12 = 0[/tex]

Take 4 as a common term,

[tex]4 (2m^2 + 5m - 3) = 0[/tex]

Since, [tex]4 \neq 0[/tex]

[tex]2m^2 + 5m - 3 = 0[/tex]

Apply the factoring method in the above equation,

[tex]2m^2 + 5m - 3 = 0[/tex]

[tex]2m^2 + (6 - 1)m - 3 = 0[/tex]

[tex]2m^2 + 6m - m - 3 = 0[/tex]

[tex]2m (m + 3) - 1(m + 3) = 0[/tex]

[tex](2m - 1) (m + 3) = 0[/tex]

This gives two solutions,

[tex]2m - 1 = 0\\2m = 1\\m = \dfrac{1}{2}[/tex]

[tex]m + 3 = 0\\m = - 3[/tex]

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The possibility statements are:

Statement 1

The function is defined on [2.4]

The above means that, the minimum is 2, and the maximum is 4

However, since the function is continuous at [2,4), the close bracket ")" means that the function extends indefinitely i.e. no maximum.

Hence, this statement is possible

Statement 2

The function is defined on [4.5]

The above means that, the minimum is 4, and the maximum is 5

However, since the function is continuous at [4,5], the close brackets "[" and "]" mean that the function have finite values

Hence, this statement is possible

Statement 3

The function is defined on [2,5]

The above means that, the minimum is 2, and the maximum is 5

However, since the function is continuous at [2,5], the close brackets "[" and "]" mean that the function have finite values and it has bounded intervals

Hence, this statement is not possible

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Let

x------> the biggest number

y------> the middle number

z------> the smallest number

we know that

[tex]x=2y[/tex] -------> equation [tex]1[/tex]

[tex]x+y=4z[/tex] -------> equation [tex]2[/tex]

[tex]z+y=x-2[/tex] -------> equation [tex]3[/tex]

substitute equation [tex]1[/tex] in equation [tex]2[/tex] and equation [tex]3[/tex]

[tex][2y]+y=4z[/tex] ------> [tex]3y=4z[/tex] ------> equation [tex]4[/tex]

[tex]z+y=[2y]-2[/tex] ----> [tex]z+2=y[/tex] ------> equation [tex]5[/tex]

using a graph tool-----> to resolve the system of equations

see the attached figure

the solution is the point [tex](6,8)[/tex]

[tex]z=6\\y=8[/tex]

Find the value of x

[tex]x=2y[/tex]

[tex]x=2*8=16[/tex]

therefore

the answer is

the biggest number is [tex]16[/tex]

the the middle number is [tex]8[/tex]

the smallest number is [tex]6[/tex]