You are driving from your house to your office. Currently, it is 7:10 a.m., and you are 12 miles from your office. If you travel at an average speed of 30 miles per hour, at what time should you arrive at your office

Answer:

784 cats      Yikes !

Step-by-step explanation:

d/c = 3/8  

              3/8 = 294/c

                        c = 294 * 8/3 = 784 cats

Using the combination formula, the coach can make 5,005 different groups.

The position does not matter, hence the combination formula is used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 6 students are taken from a set of 15, hence the number of groups is:

[tex]C_{15,6} = \frac{15!}{6!9!} = 5005[/tex]

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The extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.

In the question, we are given a graph showing the bird population of a large lake and are asked the reason for the extreme drop between November and December most likely represent.

Birds migrate in order to shift from low-resource regions to high-resource areas or vice versa. The two main items sought after are food and places to build nests.

Thus, the fall in the graph for the number of birds between November and December represents the migration pattern of birds, in search of new resources.

Hence, the extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.

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Answer: A reflection of the migratory nature of the birds at the lake.

Answer:

  (a)  3

Step-by-step explanation:

The fundamental theorem of algebra tells you a polynomial has a number of roots equal to its degree.

The degree of a polynomial is the largest exponent of the variable. Here, the degree is 3. That means there are three roots.

In general, the roots of a polynomial with real coefficients will be real or pairs of complex roots. The attached graph shows the roots of this cubic function are all real (and irrational).

The height is changing by 0.5 each minute

The question implies that we calculate the slope of the table

From the table of values, we have the following points

(0, 150) and (1, 150.5)

The slope is then calculated as:

m = (y2 - y1)/(x2 -x1)

This gives

m = (150.5 - 150)/(1 - 0)

Evaluate

m = 0.5

Hence, the height is changing by 0.5 each minute

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1a) f(x) = -1/3(x + 12)² + 9

1b) f(x) = -1/3x² - 8x - 39

Lets simplify it,

Expand by FOIL (First Outside Inside Last)

Standard Form: ax² + bx + c = 0

Transformations Graph: f(x) = a(bx - c)² + d

Reflected down and vertically stretched by 1/3:   a = -1/3

Shifted vertically by 9 units:   d = 9

Shifted horizontally by -12 units:   c = -12

Vertex Form:

 f(x) = a(bx - c)² + d

 f(x) = -1/3(x + 12)² + 9

Standard Form:

f(x) = -1/3(x + 12)² + 9

f(x) = -1/3(x² + 24x + 144) + 9

f(x) = -1/3x² - 8x - 48 + 9

f(x) = -1/3x² - 8x - 39

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Answer:

2/3 is the fraction of students who are boys.

Step-by-step explanation:

First of all, a fraction consists of two parts: The denominator and the numerator. The denominator is the whole, while the number is a part of the whole (and sometimes above).

1. Since in your question, there are 24 students in total in the class, the denominator will be 24.

2. You said that 16 of them are boys, so 16 is the numerator.

3. In a fraction, it will be 16/24.

4. 16/24 can be simplified into 2/3 since both 16 and 24 can be divided by 8.

So our final answer is 2/3.

The probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

For given question,

A research center poll showed that 85 percent of people believe that it is morally wrong to not report all income on tax returns.

so, the probability that someone have this belief is P = 0.85

We know that in probability,

p = 1 - q

where;

p is probability of success

q is probability of failure.

Thus the probability that someone does not have this​ belief would be,

= 1 - P

= 1 - 0.85

= 0.15

Therefore, the probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

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Answer:

(326-6) ÷ 8 = s

40 = s

Step-by-step explanation:

By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.

In this question we should simplify a rational number into its simplest form based on two facts. First, that all natural numbers except 1 and the prime numbers are products of prime numbers and, second, the simplification of the fraction can be done by using the following algebra property:

(a · c)/(b · c) = a/b, where a, b, c are natural numbers.     (1)

Along with power properties.

Now we proceed to simplify the rational number:

48/192 = (2⁴ × 3) / (2⁶ × 3)

48/192 = 1 / 2²

48/192 = 1 / 4

By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.

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Answer:

4

Step-by-step explanation:

Rearranging the equation so q is the independent variable is; q = -1.6r

We are given the expression;

-7q + 12r = 3q - 4r

Since we want to make q the subject, let us rearrange the equation with variables having q on the left and others on the right side to get;

-7q - 3q = -4r - 12r

-10q = -16r

q = 16r/10

q = -1.6r

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By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.

An even number can be defined as a type of number which is divisible by two (2) without any remainder.

Since this 2-digit numbers are even and its digits are distinct, we can infer and logically deduce the following points:

By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.

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A survey of 969 adult investors asked how often they tracked their portfolio. The probability that an adult investor tracks his or her portfolio daily is 0.238.

From the table it is clear that the number of responses daily by the adult investors is 231.

Probability is the ration of the number of possible value to the total value.

Here the number of daily response by the adult investors = 231

The total adult investors = 969

Hence, the The probability that an adult investor tracks his or her portfolio daily = 231/969 = 0.238.

Therefore, in the total number of 969 adult investors, the probability that the investors response daily is 0.238.

Disclaimer: The question is incomplete. The following is the correct question.

Question: Recently, the stock market took big swings up and down. A survey of 969 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily

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Answer:

C. Radius or diameter must be known.

Step-by-step explanation:

The radius or diameter must be known so you can use the formula.

Hope this helps!

The p value for the difference is 0.005.

According to the statement

we have given that the 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor.

And we have  to find the difference between them in proportions.

So,

X1 = 74 represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

X2 = 70 represent the number of people suburban residents are in favor

N1  = 100 sample 1 selected

N2 = 125 sample 2 selected

AND

P1 = 0.74 represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

And P2 = 0.56 represent the proportion of suburban residents are in favor And z would represent the statistic (variable of interest)  

Pv represent the value for the test (variable of interest)

Here we apply the Z test to find the difference then

Z = (0.74 - 0.56) / (0.64(1-0.64)(1/100+1/125) )^1/2

Now after solving

Z = 2.795.

Now The significance level provided is  ,and we can calculate the p value for this test.  

Since is a two tailed test the p value would be:  

P = (z>2,795)

P = 0.005.

So, The p value for the difference is 0.005.

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Answer:

$96.

Step-by-step explanation:

5/6  costs 80

Multiply both parts by 6/5:

5/6 * 6/5 ( = 1 ) costs 80 * 6/5

= 16 * 6

= $96.

Answer:

[tex]x^2+7x-8-\frac{3}{x-7}[/tex]

Step-by-step explanation:

I think this question is a bit hard to explain by typing, so I'll add an image down below.  

I used long division for this question, and the final answer is: [tex]x^2+7x-8-\frac{3}{x-7}[/tex]

The correct option is C. Isolating a variable in one of the equations.

The first step in solving a system of nonlinear equations by substitution is to isolate a variable in one of the equations.

A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations.

The method to solve a system of nonlinear equations by substitution is-

The importance of systems of nonlinear equations are-

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The complete question is-

Which is most likely the first step in solving a system of nonlinear equations by substitution?

A. Substituting a number for one of the variables

B. Substituting one equation into the other equation

C. Isolating a variable in one of the equations

D. Taking the square root of both sides of one of the equations

Answer:

Isolating a variable in one of the equations.

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

[tex]2logx=log64\\logx^2=log64[/tex]

now that both sides has log, you can remove them and leave it as:

[tex]x^{2} =64\\[/tex]

take the square root of both sides:

[tex]x = [8, -8]\\x = 8[/tex]

logarithmic equations can't have negative solutions, plus -8 isn't an option

i hope this helped!

The solution of the system is:

x = 62/7

y = 30/7

Here we have the system:

4x + 5y = -14

-5x - 8y = 10

To solve it by combining the equations, we need to try to remove one of the variables.

If we take the sum of 5 times the first equation and 4 times the second equation we get:

5*(4x + 5y) + 4*(-5x - 8y) = 5*(-14) + 4*10

If we simplify that we get:

20x  + 25y - 20x - 32y = -30

-7y = -30

Now we can solve that for y:

y = -30/-7 = 30/7

Now to get the value of x, we can replace the value of y in any of the given equations:

Using the first one:

4x + 5y = -14

x = (-14 - 5y)/4

x = (-14 - 5*30/7)/4 = (-98/7 - 150/7)/4 = 248/28 = 124/14 = 62/7

The solution of the system is:

x = 62/7

y = 30/7

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The problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.

The weight of the cow, on solving the equation, is found to be 320 kg.

The weight of the full-grown dog = (1/8)*320 kg = 40 kg.

We assume the weight of the cow to be x kg.

The weight of a full-grown dog is given to be one-eight of a cow, that is, the weight of a full-grown dog = (1/8)*x = x/8 kg.

Thus, the sum of the weights of the full-grown dog and the cow = x/8 + x kg.

But, we are given that together, they weigh 360 kg.

This can be shown as the linear equation in the one variable:

x/8 + x = 360.

Thus, the problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.

To solve the problem, we solve the equation as follows:

x/8 + x = 360,

or, (9/8)x = 360 {Simplifying},

or, x = 360*8/9 {Cross-Multiplying},

or, = 320.

Thus, the weight of the cow, on solving the equation, is found to be 320 kg.

The weight of the full-grown dog = (1/8)*320 kg = 40 kg.

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Answer: [tex]\theta=\frac{8}{3} \text{ radians}[/tex]

Step-by-step explanation:

[tex]8=3\theta\\\\\theta=\frac{8}{3} \text{ radians}[/tex]

Answer:

-3

Step-by-step explanation:

look at the hint: slope (most call it gradient) = change in y/change in x

so you take 2 x and y variables and subtract

15 - 9 = 6   ← change in y

0 - 2 = -2   ← change in x

slope (gradient) = 6/-2

slope (gradient) = -3

The mean is μ=140.

The standard deviation is σ = 6.4807.

The probability that X (number of successful treatments) is 128 or less is 0.0322.

In statistics, a normal distribution's probability density function is represented by a symmetrical bell-shaped curve. The likelihood that the random variable will fall between two values that define a vertical portion of the curve is represented by the area of the section.

According to the question,

An allergy medication is successful in treating 70%

The medication is given to 200 patients.

Thus,

The random variable X is a binomial random variable with n = 200 (there were 200 patients).

The probability that a medication is successful in treating a randomly selected patient is 0.7.

p = 0.7 (the medication was successful in 70% cases).

Step 1: Use the formulas for mean and standard deviation of a binomial random variable X.

[tex]\begin{gathered}\mu=E(X)=n \cdot p \\\sigma=\sqrt{n \cdot p \cdot(1-p)}\end{gathered}[/tex]

Substitute values of 'n' and 'p' to get the result,

[tex]\begin{gathered}\mu=200 \cdot 0.7=140 \\\sigma=\sqrt{200 \cdot 0.7 \cdot 0.3}=\sqrt{42}=6.4807 .\end{gathered}[/tex]

Thus, the mean is obtained as 140.

The standard deviation is 6.4807.

Step 2: find P(X≤128)

As a result, the prerequisites for a normal approximation to the binomial distribution are satisfied.

[tex]$n \cdot p=200 \cdot 0.7=140 \geq 10$$$n \cdot(1-p)=200 \cdot 0.3=60 \geq 10 .$$[/tex]

[tex]\begin{aligned}P(X \leq 128) & \approx P\left(Z \leq \frac{128-n \cdot p}{\sqrt{n \cdot p \cdot(1-p)}}\right)=P\left(Z \leq \frac{128-200 \cdot 0.7}{\sqrt{200 \cdot 0.7 \cdot(1-0.7)}}\right) \\&=P(Z \leq-1.85)=0.0322\end{aligned}[/tex]

Therefore, the probability that X is 128 or less. is 0.0322.

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The complete question is-

An allergy medication is successful in treating 70% of all patients who use it. The medication is given to 200 patients. Let X = number of successful treatments. What are the mean and standard deviation of X? Use the normal curve to approximate the probability that X is 128 or less.

The equation that runs through the location (4,-6) has the slope-intercept form,  [tex]y=-\frac{3}{4}x-3[/tex] .

A line's equation written in the slope-intercept form:

y=mx+b

where m= slope & b= y-intercept

The slope of two parallel lines is equal.

Currently, we know the line's equation:

[tex]y=-\frac{3}{4} x-5[/tex]

here, slope, m= [tex]-\frac{3}{4}[/tex]

A line equation is created by adding the slope's value and the point's coordinates (4, -6):

[tex]-6=-\frac{3}{4}(4)+b[/tex]

⇒ -6=-3 +b [adding 3 to both sides]

⇒-3=b

⇒b= -3

Hence the solution is  [tex]y=-\frac{3}{4}x-3[/tex] .

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Answer:

False

Step-by-step explanation:

They both have 1 solution

15x + 4 = 3(6x +5)

15x +4 = 18x + 15  Multiple everything in the parentheses by 3.

4 = 3x + 15  Subtract 15 x from both sides

-11 = 3x   Subtract 15 from both sides

-11/3 = x  Divide both sides by 3

There is only one solution for this equation.

2x -8 = 8x + 36

-8 = 6x + 36  Subtract 2x from both sides

--44 = 6x  Subtract 36 from both sides

-44/6 = x Divide both sides by 6.

There is only one solution for this equation.

Answer:

false

Step-by-step explanation:

They both have solutions

The number of quarts of orange juice did Rebecca use is 7

Given that 28 glasses with orange juice are filled for a camp breakfast

Each glass holds 1 cup of juice

We need to find the number of quarts of orange juice did Rebecca use  

We know that a quarts has 4 cups

We need to calculate the quarts from 28 glasses  

Let the number of the quarts be x

So the equation formed is

4x = 28

Where x is number of quarts and 28 are the number of glasses

x = 7

Hence the number of quarts is 7

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The number of prints that the probability of producing at least one quality print is 22.

Given that the probability of producing a high-quality color print is 0.10.

The binomial distribution summarizes the number of trials or observations when each trial has an equal chance of reaching a certain value. The binomial distribution determines the probability of observing a particular number of positive results in a defined number of tests.

Probability of high-quality color print (P) = 0.1

Probability of producing not high-quality color print (1-P) = 0.9

Assume the no. of prints to produce 'n' and these are produced independently say 'x' be the no. of producing quality prints, which follows a binomial distribution.

The probability function of binomial distribution is

[tex]P(X=x)\left(\begin{array}{l}n\\ x\end{array}\right)P^x(1-P)^{n-x},x=0,1,2,.....,n[/tex]

Given that

P(X≥1)≥0.90

1-P(X=0)≥0.90

1-(1-P)ⁿ≥0.90

1-(0.90)ⁿ≥0.90

(0.90)ⁿ≥0.10

Now, taking log of both sides, we get

nlog(0.90)≥log(0.10)

n(0.1053)≥2.3025

n≥21.86

n≈22

Hence, the probability of producing a high-quality color print is 0.10 and the number of prints to produce so that the probability of producing at least one quality print is larger than 0.90 is 22.

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The volume of the given composite solid is 375 m³

From the question, we are to determine the volume of the composite solid

The volume of the composite solid = Volume of the cuboid + Volume of the triangular prism

Thus,

Volume of the composite solid = (5 × 5 × 13) + 1/2(5 × 4 × 5)

Volume of the composite solid = 325 + 50

Volume of the composite solid = 375 m³

Hence, the volume of the given composite solid is 375 m³

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