A football team must move the ball forward at least 10 yards from its starting point to
make a first down. If the team has 3 losses of 2 yards each and a gain of 12 yards, does
the team make a first down?
How many yards were gained all
together

Answer:

Since a₁ = 36 and d = 1/3 the formula for this geometric sequence is aₙ = 36(1/3)ⁿ⁻¹ which means a₆ = 36 * 1/3⁵ = 0.148.

The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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Answer:From the given information, we know that after sailing for 2 hours, Alvin and his friends are 10 miles from shore. This can be written as y = 10 when x = 2.

Since there is a proportional relationship between x and y, we can write an equation using this information: y = kx, where k is the proportionality constant.

Substituting the known values, we get: 10 = k * 2

Solving for k, we get: k = 10/2 = 5

So, the equation relating x and y is: y = 5x

To find their distance from shore after sailing for 3 hours, we can plug in x = 3 into the equation:

y = 5x

y = 5 * 3

y = 15

So, after sailing for 3 hours, Alvin and his friends are 15 miles from shore.

Step-by-step explanation:

The graph of the piece-wise function f(x) is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

The extreme points of the function in this problem are given as follows:

Hence the graph of the function in this problem is composed as follows:

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Answer:

m=9

Step-by-step explanation:

brainliest pls

Question Given :

To find the value of m in ,

\(\implies\tt{2(m+2)=22}\)

Solution :

\(\mapsto\tt{2(m+2)=22}\)

\(\mapsto\tt{2{\times{m}+2\times2=22}}\)

\(\mapsto\tt{2m+4=22}\)

\(\mapsto\tt{2m=22-4}\)

\(\mapsto\tt{2m=18}\)

\(\mapsto\tt{} m = \dfrac{{ \cancel{18}}^{ \: 9} }{{ \cancel{2}}^{ \: 1} } \)

\(\mapsto\tt{m=9}\)

________________________

\(\boxed{\sf{\green{★Verification:}}}\)

Equation given :

\(\mapsto\tt{2(m+2)=22}\)

Putting the value of m in the equation :

\(\leadsto\tt{2(9+2)=22}\)

\(\leadsto\tt{2{\times(9+2)=22}}\)

\(\leadsto\tt{2\times11=22}\)

\(\leadsto\tt{22=22}\)

Hence,our L.H.S. = R.H.S.

Thus, Verified.

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Alysha would need approximately $34,234.59 in her bank account right now to be sure she always has enough for rent.

To calculate how much money Alysha would need in her bank account, we need to consider the monthly rent of $850 and the requirement to pay the first and last month's rent up front.

Since Alysha is renting for three years, she will need to pay rent for 36 months. This means she will need to have enough money to cover 36 months of rent.

To calculate the future value of her required funds, we can use the formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Here, the present value is the total amount of rent Alysha needs to cover (36 * $850), the interest rate is 3.0% (or 0.03), and n is the number of compounding periods (36).

Using the formula, the future value of Alysha's required funds would be:
Future Value = (36 * $850) * (1 + 0.03)³⁶

Simplifying this calculation, Alysha would need approximately $34,234.59 in her bank account right now to be sure she always has enough for rent.

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If it rained on Monday, Tuesday, Thursday and Friday Last week then probability of rain would be 4/7 as there are 7 days in a week.

Total days in week = total outcome = 7days
Possible outcome = 4
P(rain) = 4/7

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Answer:

13.  \(x^2+y^2+2x-3\sqrt{x^2+y^2}=0\)

14.  \(r=3\cos(\theta)-2\sin(\theta)\)

Step-by-step explanation:

Question 13

Conversion from Polar equation to rectangular equation:

\(x=r \cos(\theta) \implies \cos(\theta)=\dfrac{x}{r}\)

\(y=r \sin(\theta) \implies \sin(\theta)=\dfrac{y}{r}\)

\(x^2+y^2=r^2 \implies r=\sqrt{x^2+y^2}\)

Given:

\(r=3-2\cos(\theta)\)

\(\textsf{Substitute }\cos(\theta)=\dfrac{x}{r}:\)

\(\implies r=3-\dfrac{2x}{r}\)

Multiply both sides by r:

\(\implies r^2=3r-2x\)

\(\implies r^2+2x-3r=0\)

\(\textsf{Substitute }x^2+y^2=r^2\:\textsf{and }r=\sqrt{x^2+y^2}:\)

\(\implies x^2+y^2+2x-3\sqrt{x^2+y^2}=0\)

---------------------------------------------------------------------------------------------

Question 14

Conversion from Rectangular equation to polar equation:

\(x=r \cos(\theta)\)

\(y=r \sin(\theta)\)

\(x^2+y^2=r^2 \implies r^2\cos^2(\theta)+r^2\sin^2(\theta)=r^2\)

Given:

\(x^2+y^2-3x+2y=0\)

\(\textsf{Substitute }x^2+y^2=r^2\:\textsf{and }x=r \cos(\theta)\:\textsf{and }y=r \sin(\theta):\)

\(\implies r^2-3r\cos(\theta)+2r\sin(\theta)=0\)

Factor out common term r:

\(\implies r(r-3\cos(\theta)+2\sin(\theta))=0\)

Divide both sides by r:

\(\implies r-3\cos(\theta)+2\sin(\theta)=0\)

Rewrite to make r the subject:

Answer:

$25,740

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year,

then, solving our equation

I = 23400 × 0.05 × 2 = 2340

I = $ 2,340.00

The simple interest accumulated

on a principal of $ 23,400.00

at a rate of 5% per year

for 2 years is $ 2,340.00.

-2x + 17y + 7z - 18 = 0

This is the scalar equation of the plane.

To determine a scalar equation of the plane defined by the vector equation [x, y, z] = [1, 1, 1] + s[2, 1, 3] + t[-3, 2, 4], we need to find the normal vector to the plane.

The normal vector can be found by taking the cross product of the direction vectors in the vector equation. Let's calculate it:

[2, 1, 3] × [-3, 2, 4] = (1 * 4 - 3 * 2)i - (2 * 4 - 3 * (-3))j + (2 * 2 - 1 * (-3))k

                    = -2i + 17j + 7k

So, the normal vector to the plane is N = [-2, 17, 7].

Now, we can write the scalar equation of the plane using the normal vector N and a point on the plane (1, 1, 1):

N · ([x, y, z] - [1, 1, 1]) = 0

Substituting the values, we have:

[-2, 17, 7] · ([x, y, z] - [1, 1, 1]) = 0

Expanding the dot product:

-2(x - 1) + 17(y - 1) + 7(z - 1) = 0

Simplifying:

-2x + 2 + 17y - 17 + 7z - 7 = 0

-2x + 17y + 7z - 18 = 0

This is the scalar equation of the plane.

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Answer:

Step-by-step explanation:

The same x-coordinate (-4) means that AB is parallel to X-axis, so the distance is the difference between the larger y-coordinate and the smaller one:

-7 < 9

d = 9 - (-7) = 9 + 7 = 16

There are 35% sixth-graders at Kendrick's school who picked the museum.

Percentage is a part of the whole number.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage.

1 %= 1/100.

Given that,

Total number of sixth-graders at Kendrick's school = 56,

Also,

The number of s sixth-graders that picked the museum = 14.

The percentage of the sixth-graders that picked the museum

= (14/56) x 100

= (1/4) x 100

= 25 %

25 percent of the sixth-graders picked the museum.

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Answer: 6

Step-by-step explanation:

Conversion a mixed number 4 1/2 to a improper fraction: 4 1/2 = 4 1/2 = 4 · 2 + 1/2 = 8 + 1/2 = 9/2

To find a new numerator:

a) Multiply the whole number 4 by the denominator 2. Whole number 4 equally 4 * 2/2 = 8/2

b) Add the answer from the previous step 8 to the numerator 1. New numerator is 8 + 1 = 9

c) Write a previous answer (new numerator 9) over the denominator 2.

Four and one half is nine halfs.

Add: 6/4 + 9/2 = 6/4 + 9 · 2/2 · 2 = 6/4 + 18/4 = 6 + 18/4 = 24/4 = 4 · 6/4 · 1 = 6

bh, where b is the base and h is the height of the parallelogram.

In the case of the circle, the base of the parallelogram is the circumference of the circle, which is equal to 2πr, where r is the radius of the circle. The height of the parallelogram is the distance from the center of the circle to the edge of the circle, which is also the radius r. Therefore, we have:

b = 2πr

h = r

Substituting these values into the formula for the area of a parallelogram, we get:

Area = bh = (2πr)(r) = 2πr^2

So the formula for the area of a circle is derived from the formula for the area of a parallelogram by using the circumference of the circle as the base and the radius of the circle as the height.

Answer:

630 000

Step-by-step explanation:

We have to find 18% of the number 3 500 000:

\( \frac{3500000 \times 18\%}{100\%} = 630000\)

Answer:

1/3 and 6/18 their relationship is 6

Step-by-step explanation:

I think this might be the answer but I was confused as to what it meant as well. Sry if it’s wrong :(

The vertex of the Quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

The vertex of a quadratic function given the y-intercept and x-intercept, we need to determine the axis of symmetry, which is the line that passes through the vertex. The x-coordinate of the vertex will be the midpoint between the x-intercepts, while the y-coordinate will be the same as the y-intercept.

Given that the y-intercept is (5, 0) and the x-intercept is (0, 80), we can determine the x-coordinate of the vertex by finding the midpoint of the x-intercepts. The x-coordinate of the midpoint is simply the average of the x-values:

x-coordinate of vertex = (0 + 0) / 2 = 0 / 2 = 0

Since the y-coordinate of the vertex is the same as the y-intercept, the vertex will have the coordinates (0, 0).

Therefore, the vertex of the quadratic function is (0, 0).

In conclusion, the vertex of the quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

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Answer:

A is -3 units B is 3 units which mean -3 + 3= 0

Step-by-step explanation:

Single Sampling Plan: AQL = 0, LTPD = 3.41, AOQ = 1.79 Double Sampling Plan: AQL = 0, LTPD = 2.72, AOQ = 1.48

The values for the ASN (Average Sample Number) curves for the given single sampling plan and double sampling plan are:

Single Sampling Plan (n=80, c=3):

ASN curve values: AQL = 0, LTPD = 3.41, AOQ = 1.79

Double Sampling Plan (n1=50, c1=1, r1=4, n2=50, c2=4, r2):

ASN curve values: AQL = 0, LTPD = 2.72, AOQ = 1.48

The ASN curves provide information about the performance of a sampling plan by plotting the average sample number (ASN) against various acceptance quality levels (AQL). The AQL represents the maximum acceptable defect rate, while the LTPD (Lot Tolerance Percent Defective) represents the maximum defect rate that the consumer is willing to tolerate.

For the single sampling plan, the values n=80 (sample size) and c=3 (acceptance number) are used to calculate the ASN curve. The AQL is 0, meaning no defects are allowed, while the LTPD is 3.41. The Average Outgoing Quality (AOQ) is 1.79, representing the average quality level of outgoing lots.

For the equally effective double sampling plan, the values n1=50, c1=1, r1=4, n2=50, c2=4, and r2 are used. The AQL and LTPD values are the same as in the single sampling plan. The AOQ is 1.48, indicating the average quality level of outgoing lots in this double sampling plan.

These ASN curve values provide insights into the expected performance of the sampling plans in terms of lot acceptance and outgoing quality.

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Let's set up the variables for the two numbers --> 'a' , 'b'

Now let's set up some equations based on the given information:

Equations:

   Solve (equation 1) for b in terms of a

     b = a - 6 -- equation 3

    (equation 3) into (equation 2)

     a^2 + (a - 6)^2 = 90

     a^2 + a^2 - 12a + 36 = 90

     2a^2 - 12a - 54 = 0

     (2a + 6)(a - 9) = 0

       a = -3 -- equation 4

       a = 9 -- equation 5

    (equation 4) into (equation 1)

      -3 + b = 6

       b = 9  - ---   a = -3, b= 9

    (equation 5) into ( equation 1)

     9 + b = 6

     b = -3 - ---     a = 9, b= -3

Since the numbers are interchangeable, the two numbers are -3 and 9.

Hope it helps!

Answer:

Answer is the second bullet

Step-by-step explanation:

The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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Answer:

10%

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

EF=10

Step-by-step explanation:

If they are corresponding,

AB = 2 x Scale factor of 5 = 10

Answer:

y = 44

Step-by-step explanation:

First, add 2 on both sides to get y/4 = 11, then multiply 4 on both sides to get y = 44.

Hope this helps :)

a) The effective rate of interest on a mortgage at 8.15 percent compounded semi-annually is 8.23 percent.

b) It will take approximately 54.4 years to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly.

a) To find the effective rate of interest, we use the formula: Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods))^Number of Compounding Periods - 1.

For a mortgage at 8.15 percent compounded semi-annually, the nominal rate is 8.15 percent and the number of compounding periods is 2 per year.

Plugging these values into the formula, we get Effective Rate = (1 + (0.0815 / 2))^2 - 1 ≈ 0.0823, or 8.23 percent. Therefore, the effective rate of interest on the mortgage is 8.23 percent.

b) To determine how long it will take to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly, we can use the formula for the future value of an ordinary annuity: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of periods.

Rearranging the formula to solve for n, we have n = log(FV * r / P + 1) / log(1 + r). Plugging in the values $1,000,000 for FV, $200 for P, and 6 percent divided by 12 for r, we get n = log(1,000,000 * (0.06/12) / 200 + 1) / log(1 + (0.06/12)) ≈ 54.4 years.

Therefore, it will take approximately 54.4 years to save $1,000,000 for retirement under these conditions.

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Solution:

Given:

This is the equation of a horizontal line.

The slope of a horizontal line is 0.

Comparing the equation to equation of a line in slope-intercept form,

Therefore, the slope, m = 0

The slope of y = 10 is 0.

Answer:

your answer should be 3