Zöe schedules advertising for a radio station. She must fill 12 minutes each hour with 30 second ads and 60 second ads. Zöe sold twice as many 60 second ads as she did 30 second ads. She defines x as the number of 30 second ads and y as the number of 60 second ads that she sold. Zöe writes the system    and . Which statement identifies Zöe’s error and the correction that is needed?  Zöe used seconds to measure time for each ad, but she used minutes for the total. She should have used . Zöe set up an equation that would translate to “twice the number of 30 second ads = the number of 60 second ads.”  She should have used . Zöe compared the number of 30 second ads to the number of 60 second ads without  including the total number of ads. She should have used . Zöe did not include the whole hour in the total time. She should have used .

We want to find the solution for the system of linear equations such that we know some points of the lines. We will see that the correct option is A: (-7, 4).

When we have a system of equations the solutions are the points where the graphs of the equations intercept.

Here we know that we have two lines:

So we already can see that both lines pass through the point (7, -4), meaning that the lines do intercept at that point, so the solution of the system is that point (we know that we don't have more solutions because lines intercept only once).

So the correct option is A: (-7, 4)

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Answer:

220

Step-by-step explanation:

Lacey's mom makes her a birthday cake in the shape of an "L" . Lacey loves frosting, so her mom covers the entire outside of the cake in frosting, even the bottom of the cake.

How much space does Lacey's mom cover in frosting?

The surface area of the the cake is made up of rectangles. The formula for find the area of a rectangle is A = lw

We can divide the top of the cake into 2 rectangles.

The rectangle on the left is 12 inches by 4 inches.

A=lw

A=12*4

A=48

​  

There is a rectangle this size on the top and bottom of the cake, so we can multiply to find the area of both. 20*2=40

The rectangle on the right is 5 inches by 4 inches. We can use the formula A = lw to find the area.

​    

A=lw

A=5*4

A=20

​  

There is a rectangle this size on the top and bottom of the cake, so we can multiply to find the area of both.

48*2=96

Now we need to add in the area of the rectangles that make the sides of the cake. Let's look at the sides of the large rectangle first.

The total for these 3 surfaces is 48 .

Now let's look at the 3 remaining rectangles.

The total for these 3 surfaces is 36.

Now let's add all the surfaces together.

96+40+48+36=220

The surface area of Lacey's cake is 220 inches

There 288 ways the car can be ordered.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Given:

There are five Categories as

Total colors for car= 9

Now, the possible number of ways can it be ordered

= 9 x 2 x 2 x 2 x 2 x 2

= 9 x 32

= 288 ways

Hence, there 288 ways the car can be ordered.

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Final answer:

To determine the number of ways a car model can be ordered based on given feature choices, multiply the number of options for each feature. In this case, it's 9 colors multiplied by 2 options for each of the 5 binary features (with or without), leading to a total of 288 different combinations.

Explanation:

To determine the number of different ways a car can be ordered based on the given options, we simply need to multiply the number of choices available for each feature.

First, there are 9 colors. Then for each feature such as air conditioning, sunroof, automatic transmission, spoiler, and anti-lock brakes, there are two options available: with or without.

So, for each of these five binary options (yes or no), we multiply the number of choices by 2 (with or without).

Colors: 9 choices

Air conditioning: 2 choices

Sunroof: 2 choices

Automatic transmission: 2 choices

Spoiler: 2 choices

Anti-lock brakes: 2 choices

Now, we can calculate the total number of ways the car can be ordered:

Total ways = 9 (colors) * 2 (air conditioning) * 2 (sunroof) * 2 (automatic transmission) * 2 (spoiler) * 2 (anti-lock brakes)

Total ways = 9 * 25 = 9 * 32 = 288.

Therefore, there are 288 different combinations in which the car can be ordered.

Final answer:

The approximate volume of a cone with a radius of 9 cm and a height of 15 cm, calculated using the formula for the volume of a cone, is closest to option A, which is 1272 cm³.

Explanation:

To find the approximate volume of a cone, we use the formula V = 1/3 πr²h, where V is the volume, r is the radius of the base, and h is the height of the cone. Given that the dimensions provided are 9 cm for the radius and 15 cm for the height, the calculation is as follows:

V = 1/3 π (9 cm)² (15 cm) = 1/3 π (81 cm²) (15 cm)

Now multiply these values:

V = 1/3 π (1215 cm³) ≈ 1/3 (3817.005 cm³) ≈ 1272.335 cm³

The approximate volume of the cone is therefore closest to 1272 cm³, which makes the correct answer A. 1272cm³.

Answer:

74.29%

Step-by-step explanation:

A student passed 60%, or a proportion of 0.60 of the 20 quizzes he's written so far. This means he has passed [tex]0.60*20=12[/tex] quizzes so far.

Now he has written 50 quizzes and passed 80% of them, or [tex]50*.8=40[/tex] quizzes.

To find the success rate, take the number of quizzes passed and divide by total number of quizzes.

[tex]\frac{Passed}{Total}[/tex]=[tex]\frac{12+40}{20+50}[/tex]=[tex]\frac{52}{70}[/tex]=.7429

To get a percentage, multiply this proportion by 100 to get 74.29%

The fact that Anthony repeats the test [tex]n[/tex] times doesn't change anything, because he already know that you have a 50/50 chance of turning left of right.

Given that, Anthony observes that when people are leaving class, about 50% turn left and about 50% turn right.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

H represent turning left when leaving class and T represent turning right,

Both of them have a 50% probability of happening and he wants to know the probability of less than 3 turn left so we want to know the probability for only one to turn left and the probability for only two.

Only one:

If you use the fact that we have a binomial distribution, then the possibility that only one turns left is:

So, [tex]P(1)=\frac{4!}{3!} \times0.5^{4[/tex]

= 4×0.0625 = 0.25

Only two with the same reasoning.

[tex]P(2) = \frac{4!}{(2!\times2!)} \times0.0625=6\times0.0625 = 0.375[/tex]

Here you can see that the probability is bigger because here are mass  combinations that in the previous case.

So the total probability is 0.25 + 0.375 = 0.625.

The fact that he repeats the test [tex]n[/tex] times doesn't change nothing, because he already know that you have a 50/50 chance of turning left of right.

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To find the number of milligrams in 0.5 mL of a 1:1000 solution, we can set up a proportion: 1 mg / 1000 mL = x mg / 0.5 mL. Cross-multiplying, we get: x mg = (1 mg / 1000 mL) * 0.5 mL. Therefore, there are 0.0005 milligrams in 0.5 mL of a 1:1000 solution.

To determine the number of milligrams in 0.5 mL of a 1:1000 solution, we need to understand the ratio. In a 1:1000 solution, the first number represents the amount of solute (in this case, milligrams) and the second number represents the amount of solvent (in this case, milliliters). So, in a 1:1000 solution, there is 1 milligram of solute in 1000 milliliters of solvent.

To find the number of milligrams in 0.5 mL, we can set up a proportion:

1 mg / 1000 mL = x mg / 0.5 mL

Cross-multiplying, we get:

x mg = (1 mg / 1000 mL) * 0.5 mL

x mg = 0.0005 mg

Therefore, there are 0.0005 milligrams in 0.5 mL of a 1:1000 solution.

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Answer:

[tex]x(x+2)(x-15)[/tex]

Step-by-step explanation:

we have

[tex]x^{3}-13x^{2}-30x[/tex]

step 1

Factor x

[tex]x^{3}-13x^{2}-30x=x(x^{2}-13x-30)[/tex]

step 2

Find the solutions of [tex](x^{2}-13x-30)[/tex]

Complete the square

[tex](x^{2}-13x)=30[/tex]

[tex](x^{2}-13x+6.5^{2})=30+6.5^{2}[/tex]

[tex](x^{2}-13x+42.25)=72.25[/tex]

[tex](x-6.5)^{2}=72.25[/tex]

square root both sides

[tex](x-6.5)=(+/-)8.5[/tex]

[tex]x=6.5(+/-)8.5[/tex]

[tex]x1=6.5(+)8.5=15[/tex]

[tex]x2=6.5(-)8.5=-2[/tex]

so

[tex](x^{2}-13x-30)=(x+2)(x-15)[/tex]

substitute

[tex]x^{3}-13x^{2}-30x=x(x+2)(x-15)[/tex]

Answer:

4x + 3y - 7x

a2 + a2 - b

Step-by-step explanation:

Final answer:

To find cot a when cos a = 3/5 in the first quadrant, we first determine the length of the opposite side using the Pythagorean theorem, which gives us 4. Subsequently, cot a is calculated as the ratio of the adjacent to the opposite side, resulting in cot a = 3/4.

Explanation:

If cos a = 3/5 in the first quadrant, we use trigonometric identities to find cot a. First, recognize that in a right triangle, the Pythagorean theorem states a² + b² = c². Given cos a = adjacent/hypotenuse = 3/5, and the fact that we are in the first quadrant (where all trigonometric values are positive), we can solve for the opposite side using the Pythagorean theorem.

Let the opposite side be b, the adjacent side (corresponding to cos a) be 3, and the hypotenuse be 5. The equation becomes b² + 3² = 5² which simplifies to b² = 25 - 9 = 16, giving b = 4.

We know that cot a = adjacent/opposite = cos a / sin a. Thus, sin a = b / hypotenuse = 4/5. Therefore, cot a = 3/4.