An acrobat was launched toward a water tank, with an upward velocity of 48 feet per second. The launch point was 32 feet below the water level in the tank. Use the quadratic equation 0 = -16t2 + 48t – 32 to find how much time, t, it took for her to reach the water level in the tank.

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

[tex]y=2x+1.5[/tex]

If the point (1,4) is in the data set.

we need to find the residual of 1.

At x = 1,

[tex]y=2x+1.5\\\\y=2\times 1+1.5\\\\y=2+1.5\\\\y=3.5[/tex]

So, At x = 1, the value of y = 3.5

As we know that

[tex]Residual\ value=Estimate\ value-Actual\ value\\\\Residual\ value=4-3.5\\\\Residual\ value=0.5[/tex]

Hence, The residual of 1 is 0.5.

Thus, First option is correct.

 Arrange the numbers shown on the diagram into the correct category:                

                      Dog                Not dog                 Total  

Cat                     31                      10                      41

Not  Cat              24                     7                       31    

Total                    55                   17                       72

We have been given that the weight of an object on the mars varies directly as the weight of the object on earth.  

Let y be weight of an object on Mars and x be weight of an object on Earth.

[tex]\\ y=kx[/tex]

We have been given that the weight of an object on Mars is 34 pounds and weight of the same object on Earth is 90 pounds.

Putting the given values in equation we get

[tex]\\ 34=k(90)\\ \\ k=\frac{34}{90}=\frac{17}{45}[/tex]

Therefore, our equation now becomes

[tex]\\ y= \frac{17}{45}x[/tex]

Now we have been given that the weight of an object on Earth is 135 pounds and we have to find the weight of the same object on Mars,

We have been given that [tex]\\ x=135[/tex]

Putting the given values in our equation we get

[tex]\\ y= \frac{17}{45}(135)=\frac{17\cdot 135}{45}=17\cdot 3 = 51[/tex]

Therefore weight of the object on Mars will be 51 pounds.

Answer:

12.94

Step-by-step explanation:

Answer:

14 students have red hair.

Step-by-step explanation:

In Hamilton Middle School 2% of the students have red hair .

Total number of students in the school = 700

We have to calculate the number of students who have red hair.

2% of 700 students.

= [tex]\frac{2}{100}[/tex] × 700

= 0.02 × 700

= 14 students.

14 students have red hair in Hamilton Middle School.

Answer:

answer is : A. 1010

Step-by-step explanation:

Answer:

A. The interquartile range of Mitchell's data is greater than the interquartile range of Luke's data.

Step-by-step explanation:

The term population is the set containing all the people or objects whose properties are to be described. Hence, option (a) is correct.

A community is a distinct group of people, creatures, or other objects that can be recognized for the purposes of data gathering and analysis by at least one shared trait.

The majority of the time, data is collected from samples in order to learn more about huge populations. For instance, market researchers might randomly contact a small percentage of the town's subscribers to major carrier services who were born between 1980 and 2004 if they wanted to obtain representative statistics for Millennial consumers of mobile phones who did not have a landline in New York City (the population).

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The largest possible product of two odd integers whose sum is 42 is 437, obtained from multiplying 19 by 23.

The question asks for the largest possible product of two odd integers whose sum is 42. To find this, we should split 42 into two odd numbers that are as close to each other as possible because the product of two numbers that are close together will be higher than the product of a pair that has a larger difference.

If we divide 42 by 2, we get 21, which is not an even integer, so we need to adjust the numbers by 1. So the two odd numbers closest to each half of 42 are 21 and 21. However, we can't have them both be the same number since we're looking for two integers, so we adjust one up and one down by 1, resulting in 20 and 22. To ensure both numbers are odd, we will subtract 1 from the first number and add 1 to the second number, giving us 19 and 23 as the two odd integers that sum to 42.

The product of 19 and 23 is 19 × 23 = 437, which is the largest possible product for two odd integers that add up to 42.

The given sequence is a geometric sequence. Each term in the sequence multiplies by 4 to obtain the next. Therefore, the recursive formula for the sequence is an = 4 * an-1.

The given sequence is: 3, 12, 48, 192, 768, and so on. Looking at the sequence, we can see that each term is multiplied by 4 to get the next term. So, the sequence is a geometric sequence. The recursive formula for a geometric sequence is given by: an = r * an-1, where an is the nth term, r is the common ratio, and an-1 is the previous term. In this case, r equals 4 (since we are multiplying each term by 4 to get the next term). Thus, "the recursive formula for this geometric sequence is: an = 4 * an-1".

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Answer:

  64 units

Step-by-step explanation:

Segment addition holds, so we can write ...

  LM + MN = LN

  (10x +8) +(5x-4) = (12x +16)

  15x + 4 = 12x + 16 . . . . . . . . collect terms

  3x -12 = 0 . . . . . . . . . . . . . .  subtract 12x+16

  x-4 = 0 . . . . . . . . . . . . . . . . . divide by 3

  x = 4 . . . . . . . add 4

LN = 12x +16 = 12·4 +16 = 48 +16 . . . . . substitute into the expression for LN

LN = 64 . . . . units

Answer:

f(5)=37

Step-by-step explanation:

We have the function f(x)=8x-3,

f(5) is the value of the function f when x=5, then you have to replace f(x) with x=5,

f(x)=8x-3

f(5)=8.(5)-3

f(5)=40-3

f(5)=37

Answer:

True

Step-by-step explanation:

The probability of getting blue from the first box is 3/5.

Given that, a box contains 3 blue and 2 red pens while another box contains 2 blue and 5 red pens.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n.

The probability of getting blue from the first box:

The number of favourable outcomes = 3 and the number of total outcomes =5

So, P(E) = 3/5

The probability of getting blue from the second box:

The number of favourable outcomes = 2 and the number of total outcomes =7

So, P(E) = 2/7

Therefore, the probability of getting blue from the first box is 3/5.

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The equation that can be used to find the base of the triangular road sign is 60 = (b * (2b - 1)) / 2.

Let's assume that the base of the triangular road sign is represented by b. According to the problem, the height of the sign is 1 inch shorter than twice its base, which can be written as:

height = 2b - 1

The area of a triangle can be calculated using the formula Area = (base * height) / 2. Substituting the given values into the formula, we get:

60 = (b * (2b - 1)) / 2

This equation can be used to find the base, b, of the sign.

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