The scale drawing of a baby blanket has the dimensions of 6 inches by 10 inches. the dimensions of the actual baby blanket are 30 inches by 50 inches. what is the scale factor that is used to make the drawing?

Answer:

(x - 7)² + (y - 3)² = 4

Step-by-step explanation:

The equation formula of a circle is (x - h)² + (y - k)² = r², where the center is at ordered pair (h, k) and r represents the radius in units.

With the information given in the question itself, we plug and play, simplifying if need be:
center (7, 3), h = 7, k = 3
radius = 2

(x - 7)² + (y - 3)² = (2)²
(x - 7)² + (y - 3)² = 4

The equation of this circle is (x - 7)² + (y - 3)² = 4

The equation without fractions is 8x - 36 = 9.

To eliminate fractions from the equation 2/3x - 3 = 3/4, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 12:

(12) * (2/3x - 3) = (12) * (3/4)

This will clear the fractions:

2(4x) - 3(12) = 3(3)

Now, simplify each term:

8x - 36 = 9

So, the equation without fractions is:

8x - 36 = 9

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There are 2730 different ways for a club with 15 members to choose a president, vice president, and treasurer, with each office being held by a different person.

To determine the number of ways the club can choose a president, vice president, and treasurer, we can use the concept of permutations since the order of selection matters here, and no person can hold more than one office.

The first office to be filled is the president's.

There are 15 potential members to fill this role.

Once the president has been chosen, there are 14 remaining members who could be the vice president.

Finally, for the treasurer, there are 13 members left to choose from.

To find the total number of ways to choose these officers, we multiply the number of choices for each office together.

Number of ways = 15 (for president) × 14 (for vice president) × 13 (for treasurer) = 2730 ways.

So, there are 2730 different ways in which the club can select a president, vice president, and treasurer.

The exponential function is f(x) = 3(2)× which is passes throgh the two points (1,6) and (3,24).

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

We have:

An exponential function:

f(x) = c(a)×

The two points are given:

(1,6) and (3,24)

Plug x = 1

f(x) = 6

6 = c(a) ...(I)

Plug x = 3

f(x) = 24

24 = c(a)³  ...(II)

Divide equations (1) and (II)

24/6 = c(a)³/c(a)  

4 = a²

a = 2

Plug a = 2 in equation I

6 = c(2)

c = 6/2

c = 3

The exponential function:

f(x) = 3(2)×

Thus, the exponential function is f(x) = 3(2)× which is passes throgh the two points (1,6) and (3,24).

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For a better understanding of the explanation provided here kindly go through the file attached.

Since, the weight attached is already at the lowest point at time, t=0, therefore, the equation will have a -9 as it's "amplitude" and it will be a Cosine function. This is because in cosine function, the function has the value of the amplitude at t=0.

Now, we know that the total angle in radians covered by a cosine in a given period is [tex] 2\pi [/tex] and the period given in the question is t=3 seconds. Therefore, the angular velocity, [tex] \omega [/tex] of the mentioned system will be:

[tex] \omega=\frac{2\pi}{3} [/tex]

Combining all the above information, we see that the equation which models the distance, d, of the weight from its equilibrium after t seconds will be:

[tex] d=-9cos(\frac{2\pi}{3})t [/tex]

Thus, Option B is the correct option. The attached diagram is the graph of the option B and we can see clearly that at t=3, the weight indeed returns to it's original position.

Answer: B.

Step-by-step explanation:

answer on edge

What is the product of 2.31 and 0.21?

Solution:

We need to find 2.31*0.21

Let us first find 231*21, then we would consider decimals

231*1=231

231*2=462

So, 231*21=231+4620=4851

So, we get 231*21=4851

But, we need to find, 2.31*0.21

There are two numbers after decimal in 2.31 (3 and 1). and, there are two numbers after decimal in 0.21(2 and 1)

So, In result of, 2.31*0.21 there must be four digits after decimal.

As, 231*21=4851

So, 2.31*0.21=0.4851 (four digits after decimal)

Answer:0.4851

Answer:

16 cm

Step-by-step explanation:

Given : The area of triangle ABC is 24 square centimeters.

To Find: If B = 30° and a = 6 cm, what is the measure of side c?

Solution:

Formula : [tex]Area = \frac{1}{2} \times a \times c \times sin B[/tex]

a = 6

Area = 24

B = 30°

Substitute the values in the formula

[tex]24 = \frac{1}{2} \times 6 \times c \times sin 30[/tex]

[tex]24 = \frac{1}{2} \times 6 \times c \times \frac{1}{2}[/tex]

[tex]24 =3 \times c \times \frac{1}{2}[/tex]

[tex]\frac{24 \times 2}{3} =c[/tex]

[tex]16=c[/tex]

Hence the measure of side c is 16 cm

So, Option c is correct.

Answer:

The correct option is C.

Step-by-step explanation:

In a dot plot, the number of dots above a number represents the frequency of that number.

From the given dot plot it is clear that number of dots for group R is 21 and the time taken by the students of groups R are

45, 50, 50, 55, 60, 60, 70, 75, 80, 85, 90, 90, 95, 100, 100, 105, 110, 110, 115, 120, 120

The average of the data is

[tex]Average=\frac{\sum x}{n}[/tex]

[tex]Average=\frac{45+50+50+55+60+60+70+75+80+85+90+90+95+100+100+105+110+110+115+120+120}{21}[/tex]

[tex]Average=\frac{1785}{21}[/tex]

[tex]Average=85[/tex]

From the given dot plot it is clear that number of dots for group S is 17 and the time taken by the students of groups S are

50, 55, 60, 60, 65, 70, 70, 80, 90, 90, 95, 100, 105, 110, 110, 115, 120

[tex]Average=\frac{50+55+60+60+65+70+70+80+90+90+95+100+105+110+110+115+120}{17}[/tex]

[tex]Average=\frac{1445}{17}[/tex]

[tex]Average=85[/tex]

The average time of both groups are same.

Since both groups show about the same average time, therefore the correct option is C.

Answer:

No real solutions, or 0

Explanation:

We can determine how many real solutions a quadratic function has, we can use the quadratic formula.

The quadratic formula for expressions written in ax² + bx + c form is:

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

In the equation x² + 5x + 7, a = 1, b = 5 and c = 7

When we plug them in, we get:

[tex]x = \frac{-5 +/-\sqrt{5^2 - 4(1)(7)}}{2(1)}\\ \\= \frac{-5+/-\sqrt{25 - 28}}{2}\\ \\=\frac{-5+/-\sqrt{-3}}{2}}[/tex]

We cannot find the square root of a negative number without diving into the realm of imaginary numbers in which √-3 becomes i√3. Therefore, the equation has no real solutions. This is because the equation x² + 5x + 7 is an upward-facing parabola translated up 7 units and, as such, does not cross the x-axis. If the equation yields a graph that does not cross the x-axis, then there will be zero answers for what variable x equals.

Answer:

Ok so ppl it just A

Step-by-step explanation:

To solve this problem, we must first subtract 4 from both sides of the inequality. This gives us -2 ≥ -v. Next divide both sides by -1. Remember, when you divide by a negative in an inequality, it becomes necessary to flip the direction of the inequality symbol. Therefore, the answer to the inequality is 2 ≤ v, which is equivalent to v ≥ 2.

The approximate surface area of the sphere will be 707 yd^2

The steps are as follow:

r = 7.5 yd

Surface area of sphere = 4πr^2

Surface area of sphere = 4*π*(7.5)^2

Surface area of sphere = 706.85 yd^2

Surface area of sphere = 707 yd^2

So the approximate surface area of the sphere will be 707 yd^2

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Final answer:

The inequality representing the number of karate classes Theo can take is c ≤ 17, considering his budget after buying a dogi and the cost per class.

Explanation:

The question asks us to find the inequality that represents the number of karate classes, c, Theo can take given his budget scenario. Theo budgets $154 for his karate classes and spends $12 on a dogi. This leaves Theo with $154 - $12 = $142 for classes. Since each class costs $8, we divide the remaining budget by the cost per class to find the maximum number of classes he can take:

$142 ÷ $8 = 17.75.

Since Theo cannot attend a fraction of a class, we round down to 17. The inequality representing the number of classes Theo can take would be c ≤ 17, where c is the number of classes Theo can attend.

The inequality that represents the number of classes, [tex]\( c \)[/tex], that Theo can take is:

[tex]\[ 8c + 12 \leq 154 \][/tex]

To derive this inequality, we start by considering the total amount Theo has budgeted for karate classes, which is $154. From this budget, Theo has already spent $12 on purchasing a karate uniform. Therefore, the remaining amount available for attending the classes is [tex]\( 154 - 12 \)[/tex].

Now, each karate class costs $8, so the total cost for attending [tex]\( c \)[/tex] classes is [tex]\( 8c \)[/tex]. To ensure that Theo does not exceed his budget, the total cost including the uniform should be less than or equal to $154.

Hence, the inequality that represents this situation is:

[tex]\[ 8c + 12 \leq 154 \][/tex]

This inequality states that the cost of the uniform plus the cost of the classes must be less than or equal to Theo's budget. Solving for [tex]\( c \)[/tex] will give us the maximum number of classes Theo can attend without exceeding his budget.

Calculate the cost per apple for large and small baskets, $0.39 per apple is the closest estimate.

To estimate the cost per apple, one must calculate the price of each apple in the large and small baskets, then average these amounts, resulting in approximately 44 cents per apple.

To find the cost per apple:

Calculate the cost per apple in the large basket: $22.95 / 59 apples = $0.39 per apple.

Calculate the cost per apple in the small basket: $8.95 / 18 apples = $0.50 per apple.

Compare the two costs: $0.39 is the closest estimate of the cost per apple.

Answer:

[tex](x,y)\rightarrow (-x,-y)[/tex]

Step-by-step explanation:

We are asked to find the the algebraic rule describes the 180° counterclockwise rotation about the origin .

We know that when we rotate a point 180° counterclockwise rotation about the origin , the x and y-coordinates change their sign.

[tex](x,y)\rightarrow (-x,-y)[/tex]

Therefore, our required rule is [tex](x,y)\rightarrow (-x,-y)[/tex].

Lance rolls a die 5 times

In a six sided dice, the even numbers are 2, 4  and 6. So 3 even numbers

the probability that he rolls an even number = [tex]\frac{3}{6} = \frac{1}{2}[/tex]

the probability that he rolls an even number all five times

= [tex]\frac{1}{2} *\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}= \frac{1}{32}[/tex]

So answer is [tex]\frac{1}{32}[/tex]