Donna has 3 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down If she runs ata speed of 9 mph and walks back at a speed of 3 mph, how long should she plan to spend walking back?

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

More can be learned about the Factor Theorem at brainly.com/question/24729294

#SPJ1

Answer:

a) SS, Ss, ss

b) 1/4

c) 1/2

Step-by-step explanation:

According to this question, a gene coding for possession or not of sickle cell has two alleles. Allele "S" codes for normal cell while allele "s" codes for sickle cell. A heterozygous individual or carrier will have a "Ss" genotype.

If two carriers of the sickle cell condition decide to have a child and mate i.e. Ss × Ss, the following gametes will be produced by each parent: S and s.

a) Using these gametes (S, s) in a punnet square (see attached image), the four possible offsprings with the following genotypes will be produced: SS, Ss and ss in a GENOTYPIC RATIO 1:2:1.

b) Since offsprings with the genotype "ss" will possess the sickle cell condition/phenotype, the probability of offsprings that will have sickle cell is 1/4 i.e. 1 out of 4 possible offsprings

c) Also,carrier genotype will be "Ss", therefore, the probability that the offspring will not have sickle cell but still be a carrier (one normal cell allele and one sickle cell allele) will be 2/4 or 1/2 i.e. 1 out of 2 possible offsprings.

1.243 is the measure of the value of x from the given expression

Rational equations are those that contain rational expressions. A rational expression is a fraction with polynomial numerator and denominator. A rational expression, in other terms, is a ratio between two polynomials.

Given the following rational equation

√11 x = √17

We need to determine the measure of the value of x.

Taking the square of both sides we will have:

(√11 x)² = (√17)²

11x² = 17

x² = 17/11

x² = 1.545

Take the square root of both sides

√x² = √1.545
x = 1.243

Hence the measure of the value of x from the given equation is 1.243.

Learn more on rational equation here: https://brainly.com/question/12223525

#SPJ1

Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

Step-by-step explanation:

5x + 2x

that is the same as (5 + 2)x

and that is the same as (7)x = 7x

so, for the second part of the problem we are actually comparing

7x

and

7x - 1

there is therefore no way for the two expressions to deliver the same value for the same x.

the values of 7x are always larger by one than the values of 7x - 1

so, e.g.

x = 1

5×1 + 2×1 = 5 + 2 = 7

7×1 - 1 = 7 - 1 = 6

x = 2

5×2 + 2×2 = 10 + 4 = 14

7×2 - 1 = 14 - 1 = 13

x = 3

5×3 + 2×3 = 15 + 6 = 21

7×3 - 1 = 21 - 1 = 20

x = 4

5×4 + 2×4 = 20 + 8 = 28

7×4 - 1 = 28 - 1 = 27

x = 5

5×5 + 2×5 = 25 + 10 = 35

7×5 - 1 = 35 - 1 = 34

Answer:

See below

Step-by-step explanation:

Answer:

To determine the number of ways in which 4 students can be chosen for special awards out of a group of 5 high-performing students, we can use the permutation formula:

P(n,r) = n! / (n-r)!

where n is the total number of high-performing students and r is the number of students being chosen for the awards.

In this case, we have n = 5 and r = 4, so we can substitute these values into the formula:

P(5,4) = 5! / (5-4)! = 5! / 1! = 5 x 4 x 3 x 2 x 1 / 1 = 120

Therefore, there are 120 different orders in which 4 students can be chosen for the special awards out of a group of 5 high-performing students.

Step-by-step explanation:

f(x) = 3x² - 2x + 8 , x = 3

f(3) = 3.3² - 2.3 + 8

= 27 - 6 + 8

= 29

Answer:

The probability that the diagnosis is correct is 0.95249.

Step-by-step explanation:

We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.

Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.

Let the probability that people in the United States have diabetes = P(D) = 0.083.

So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917

Also, let A = event that the diagnostic test is accurate

So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98

And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95

Now, the probability that the diagnosis is correct is given by;

    Probability = P(D) \(\times\) P(A/D) + P(D') \(\times\) P(A/D')

                      = (0.083 \(\times\) 0.98) + (0.917 \(\times\)0.95)

                      = 0.08134 + 0.87115

                      = 0.95249

Hence, the probability that the diagnosis is correct is 0.95249.

The solution of the sequence aₙ = −6aₙ₋₁− 5aₙ₋₂ for n ≥ 3 with the initial conditions is a₂ = -316

From the question, we have the following sequence that can be used in our computation:

aₙ = −6aₙ₋₁− 5aₙ₋₂ for n ≥ 3

Also, we have the initial conditions of the sequence to be

aₙ = 28 and a₁ =−76

The above parameters imply that we set the value of the variable n to 2 in the equation aₙ = −6aₙ₋₁− 5aₙ₋₂

So, we have the following representation

a₂ = −6a₂₋₁− 5a₂₋₂

Evaluate the difference in the above equation

So, we have the following representation

a₂ = −6a₁− 5aₙ

Substitute the known values in the above equation, so, we have the following representation

a₂ = −6 * 76− 5 * -28

Evaluate the expression

a₂ = -316

Hence, the solution is a₂ = -316

Read more about sequence at

brainly.com/question/7882626

#SPJ1

Answer:

They will never intersect. I'm pretty sure that is right

Answer:

what is the value of X? 23

Answer:

Step-by-step explanation:

The ratio of sides for the 30/60/90 triangle is 1:3^(1/2):2

Since the side opposite the 60 degree angle is 7(3^(1/2))

x=7(1)=7

y=7(2)=14

Answer:

They are less than 1/2

Step-by-step explanation:

The answer is

a (n) = -3n +22

Answer:

Nth term: -3n+19

Step-by-step explanation:

You can see the sequence is decreasing by 3 each time so the Nth term is -3n.

The 0 term would therefore be 19 so the formula would be -3n+19.

The decimal equivalent of the largest Absolute value, 987654321, is 987,654,321.  the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.

The largest and smallest absolute values using the digits 1 to 9, we need to arrange them in a way that maximizes or minimizes the resulting number. Let's consider the boxes as placeholders for the digits.

To determine the largest absolute value:

We place the digit 9 in the leftmost box, as it is the largest digit among 1 to 9. Then we arrange the remaining digits, 8, 7, 6, 5, 4, 3, 2, and 1, from largest to smallest in the remaining boxes. This gives us the number 987654321, which is the largest possible number using the given digits. Therefore, the largest absolute value is 987654321.

To determine the smallest absolute value:

We place the digit 1 in the leftmost box, as it is the smallest digit among 1 to 9. Then we arrange the remaining digits, 2, 3, 4, 5, 6, 7, 8, and 9, from smallest to largest in the remaining boxes. This gives us the number 123456789, which is the smallest possible number using the given digits. Therefore, the smallest absolute value is 123456789.

To find the decimal equivalent of these numbers, we simply read the digits from left to right. The decimal equivalent of the largest absolute value, 987654321, is 987,654,321. The decimal equivalent of the smallest absolute value, 123456789, is 123,456,789.

Thus, the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.

To know more about  Absolute value.

https://brainly.com/question/24368848

#SPJ8

Step-by-step explanation:

\( \underline{ \underline{ \text{Given \: points}}} : \)

Let the points ( 0 , 2 ) and ( 2 , 4 ) be A and B respectively. Let A ( 0 , 2 ) ⤑ ( x₁ , y₁ ) & B ( 2 , 4 ) ⤑ ( x₂ , y₂ ). Now , Using two point form of the equation of striaght line , we have :

Plug the values :

⟶ \( \tt{y - 2 = \frac{4 - 2}{2 - 0} (x - 0)}\)

⟶ \( \tt{y - 2 = \frac{2}{2} x}\)

⟶ \( \tt{y - 2 = x}\)

⟶ \( \tt{0 = x - y + 2 }\)

\( \pink{ \boxed{ \boxed{ \bold{ \tt{our \: final \: answer : \boxed{ \underline{ \tt{x - y + 2 = 0}}}}}}}}\)

Hope I helped ! ツ

Have a wonderful day / night ! ♡

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Solution:

The points are;

We find that the quadratic model is;

The quadratic model with the coefficients rounded to three decimal places is;

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

Read more about  Laws of Exponents at: https://brainly.com/question/11761858

#SPJ1

Answer: Let's call the original price of the bracelet "P". We can set up an equation based on the given information:

P + 0.72 = 1.06P

The left side of the equation represents the total amount that Casey paid for the bracelet and sales tax. The right side of the equation represents the original price of the bracelet plus the 6% sales tax.

To solve for P, we can simplify and solve the equation:

P + 0.72 = 1.06P

Subtract P from both sides:

0.72 = 0.06P

Divide both sides by 0.06:

P = 12

Therefore, the original price of the bracelet before tax was $12.

Step-by-step explanation:

(2 one)

(2,2) is the answer

Answer:

y+4=3(x+2)

Step-by-step explanation:

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

m=(8-(-4))/(2-(-2))

m=(8+4)/(2+2)

m=12/4

m=3

y-y1=m(x-x1)

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

y+4=3(x+2)

Answer:

Step-by-step explanation:

The point ( -2 , 3) lies in the 2nd quadrant

Point are generally in the form (x , y). The point you need to plot is ( -2 , 3) which means the value of x = -2 and the value of y = 3.

I have attached an image you can check it out.

Answer:

b

Step-by-step explanation:

because it is -2 four times and if you do -2 ×4 you get -8. hope thid helped

The slope and the y-intercept of the line y = 4x + 5 are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The function for this problem is given as follows:

y = 4x + 5.

Hence the slope and the intercept are given as follows:

The problem asks for the slope and the intercept of y = 4x + 5.

More can be learned about linear functions at https://brainly.com/question/15602982

#SPJ1

Answer:

B. 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Angle = 37°

Adjacent Leg = x

Hypotenuse = 10

Step 2: Solve for x

Step-by-step explanation:

please it my steps to work on paper whorksheet

Answer:

QIII

Step-by-step explanation:

A 1.5 standard deviations above the mean IQ score is 122.5.

An expression that depicts the relationship between two or more numbers and variables is called an equation.

A dependent variable is one that depends on another variable, whereas an independent variable does not depend on any other variable for its value.

Giving the z score are:

z is calculated as (raw score - mean) / standard deviation.

with a standard deviation of 15 and a mean of 100. The z-score of 1.5 is equal to the IQ score that is 1.5 standard deviations above the mean, so:

1.5 = (x - 100)/15

x = 122.5

A 1.5 standard deviations above the mean IQ score is 122.5.

The Complete Question is IQ score.

To Learn more About IQ scores refer to:

https://brainly.com/question/28143524

#SPJ1

Amplitude is the maximum displacement of a function on a graph.

Amplitude is the maximum displacement of a function on a graph. It refers to the maximum height or distance from the baseline of a wave or oscillation.

It is often used in physics and engineering to describe the strength or size of a signal, vibration, or wave. In simple terms, it can be thought of as the "peak-to-peak" distance of a waveform, or the height of the waveform above and below the baseline.

But the minimum displacement of a function on a graph would typically be referred to as the minimum value or the "valley" of the function.

Learn more about amplitude on:

https://brainly.com/question/25699025

#SPJ1