If A is an mÃn matrix then ATA and AAT are both defined

from the picture above, we can see that the focus point of the parabola is at (2 , -4) and its vertex at (2 , -5), so the "p" distance from each other is just 1 unit, since the vertical parabola is opening upwards, that means "p" is positive or just p=1.

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\cap}\qquad \stackrel{p~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=2\\ k=-5\\ p=1 \end{cases}\implies 4(1)(~~y-(-5)~~) = (~~x-2~~)^2 \\\\\\ 4(y+5)=x^2+4x+4\implies 4y+20=x^2+4x+4 \\\\\\ 4y=x^2+4x-16\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x^2+x-4 \end{array}}[/tex]

Step-by-step explanation:

Im a fifth grader so I gave it my best shot and there might be more steps to it but I'm pretty sure its 2/10

The calculated value of the expression √97 is between 8 and 10

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

√97

The above expression is a radical expression, and at the same time it is an irrational number

This is because

When evaluated, we have

√97 = 9.848.....

This number is between 8 and 10

Hence, the value of the expression is between 8 and 10

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The probability that z lies between 0 and 3.01 is: 0.9987 - 0.5 = 0.4987 So, the answer is 0.4987. To find the probability that z lies between 0 and 3.01 for a standard normal variable, you need to look up the values in a standard normal (z-score) table or use a calculator with the normal distribution function.

For z = 0, the probability is 0.5 (due to symmetry of the standard normal distribution). For z = 3.01, the probability is approximately 0.9987. To find the probability between 0 and 3.01, subtract the probability of z = 0 from the probability of z = 3.01.

0.9987 - 0.5 = 0.4987

So, the probability that z lies between 0 and 3.01 is approximately 0.4987. Your answer is 0.4987.

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When a square pyramid is sliced in such a way that the plane passes through all five faces of the pyramid, the resulting cross-section is a pentagon.

The square pyramid has a square base and four triangular faces, so when a plane passes through all five faces, it intersects each of the four triangular faces to form a trapezoid. These four trapezoids combine to form a pentagon.

The resulting cross-section can vary depending on the angle at which the plane intersects the pyramid. If the plane intersects the pyramid at a right angle to the base, the resulting pentagon will be a regular pentagon. If the plane intersects the pyramid at an angle, the resulting pentagon will be irregular.

In summary, when a square pyramid is sliced in such a way that the plane passes through all five faces of the pyramid, the resulting cross-section is a pentagon, which can be regular or irregular depending on the angle of intersection.

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The fraction for the given situation is 7/3. Therefore, option D is the correct answer.

Given that, there are 7 apple pies.

3 people will share the pies equally.

Equal share of pie = Number of apple pies/Number of people

Equal share of pie = 7/3

So, the fraction is 7/3 of a whole

Therefore, option D is the correct answer.

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Considering the three-place Boolean function f defined

(a) f(1, 1, 1) = (7(1) + 2(1) + 4(1)) and f(0, 0, 1) = (7(0) + 2(0) + 4(1))

(b) Using an input/output table f is an odd parity function.

A Boolean function is a mathematical function that takes input values and returns a binary output value. In the given problem, the three-place Boolean function f is defined by the rule (7x1 + 2x2 + 4x3) mod 2, where x1, x2, and x3 are binary inputs.
To find f(1, 1, 1), we substitute x1=1, x2=1, and x3=1 in the given function. Therefore, f(1, 1, 1) = (7(1) + 2(1) + 4(1)) mod 2 = 1.
Similarly, to find f(0, 0, 1), we substitute x1=0, x2=0, and x3=1 in the given function. Therefore, f(0, 0, 1) = (7(0) + 2(0) + 4(1)) mod 2 = 0.
To describe f using an input/output table, we consider all possible input combinations of x1, x2, and x3 and evaluate the function for each combination. The resulting input/output table is as follows:
Input Output
x1 x2 x3 f
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
From the input/output table, we can see that the function f returns 1 when the sum of 7x1, 2x2, and 4x3 is odd and returns 0 when it is even. Thus, we can conclude that f is an odd parity function.

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Answer:

Step-by-step explanation:

b

To construct the circumcenter of triangle ABC, we need to find the point that is equidistant to its three vertices A, B, and C. We can do this by constructing the perpendicular bisectors of the sides AB, BC, and AC, and finding their intersection point.

Here are the steps to construct the circumcenter:

Draw triangle ABC.

Construct the perpendicular bisectors of sides AB and BC. To do this, find the midpoint of each side (label them M and N, respectively), and draw a perpendicular line to each side that passes through its midpoint. Label the points where the perpendicular bisectors intersect AB and BC as P and Q, respectively.

Construct the perpendicular bisector of side AC using the same method. Label the point where this bisector intersects AC as R.

Draw lines connecting each vertex of the triangle to the intersection point of the perpendicular bisectors. These lines are the radii of the circumcircle.

The intersection point of the perpendicular bisectors is the circumcenter of triangle ABC. Label this point as O.

Now, we have constructed the circumcenter O of triangle ABC, which is the point that is equidistant to its three vertices A, B, and C.

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The difference in the Beatles length is 1 / 10 centimetres.

Serena is measuring the length of beetles for a science project .One beetle measures 4/5 cm and another measure 7/10 cm.

Therefore, the difference in the beetles length can be calculated as follows:

Hence,

difference between the beetles length = 4 / 5 - 7 / 10

difference between the beetles length = 8 - 7 / 10

difference between the beetles length = 1 / 10 centimetres

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Answer:

Step-by-step explanation:

5 +2/10

since 5 is on outside you can just add them

a. To find the t-test statistic, we first need to calculate the standard error of the mean using the formula: standard deviation / square root of sample size. In this case, the standard error of the mean is 600 / square root of 50, which is approximately 84.85.

Then, we can calculate the t-test statistic using the formula: (sample mean - hypothesized population mean) / standard error of the mean. In this case, the t-test statistic is (2450 - 2600) / 84.85, which is approximately -1.77.

b. To find the P-value, we need to consult a t-distribution table or use statistical software. Using a two-tailed t-test with 49 degrees of freedom (50-1), we find that the P-value associated with a t-test statistic of -1.77 is approximately 0.084. Therefore, there is a 8.4% chance of obtaining a sample mean of $2,450 or less if the true mean amount of Pell grant awards received by San Jose State University Pell grant recipients this year is actually $2,600.

Note: A common threshold for statistical significance is a P-value of less than 0.05. Since the P-value in this case is greater than 0.05, we cannot reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean amount of Pell grant awards received by San Jose State University Pell grant recipients this year is different from $2,600.
a. To find the t-test statistic, we will use the following formula:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Here, sample mean = $2,450, population mean = $2,600, sample standard deviation = $600, and sample size = 50.

t = ($2,450 - $2,600) / ($600 / sqrt(50))
t = (-$150) / ($600 / 7.071)
t = (-$150) / $84.85
t ≈ -1.77

The t-test statistic is approximately -1.77.

b. To find the P-value, we need to use a t-distribution table or software to determine the probability of obtaining a t-test statistic as extreme or more extreme than our calculated value. We are doing a two-tailed test, so we need to find the area in both tails.

Looking up the t-test statistic -1.77 in a t-distribution table with 49 degrees of freedom (sample size - 1), we find the P-value is between 0.05 and 0.10. For a more accurate P-value, use software or an online calculator.

So, the P-value is between 0.05 and 0.10.

Answer:

16 i think

Step-by-step explanation:

Answer:

We know that

Area of rectangle: Length" Breadth

For Question

Area of respective Rectangle are:

A : 13*(x+12) ft²

B : 10*8=80ft²

C : (x+10)*7 ft²

D : (x+10)*(10-7)=(x+10)*3 ft2

E : 6*6 =36 ft²

F : 7*6= 42 ft²

G : (x+8)*(x+7) ft²

H : (3x+23)*(2x+17) ft²

I. : (2x+16)*(x+8) ft²

If P(A) = 0.7, P(B) = 0.8, and P (A or B) = 0.9 the value of P (A and B) will be 0.6.

P(A) is the probability of event A happening.

P(A) = 0.7

P(B) is the probability of event B happening.

P(B) = 0.8

P (A or B) is the probability of either A or B happening.

P (A or B) = 0.9

P (A and B) is the probability of both A and B happening.

P (A and B) =?

The formula to find the value of P (A and B) is,

P (A and B) = P(A) + P(B) - P (A or B)

P (A and B) = 0.7 + 0.8 - 0.9

P (A and B) = 1.5 - 0.9

P (A and B) = 0.6.

Therefore, the value of P (A and B) is 0.6.

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The value of m so that the condition satisfies is -2, the correct option is A.

We are given that;

y=f(x) is continuous

Now,

To find the numbers c that satisfy the conclusion of the Mean Value Theorem, we need to solve the equation:

f’© = [f(2) - f(0)] / (2 - 0)

f’(x) = 8x - 2

f(2) = 4(2)^2 - 2(2) + 3 = 23

f(0) = 4(0)^2 - 2(0) + 3 = 3

f’© = (23 - 3) / (2 - 0)

f’© = 10

8m - 2 = 10

8m = 12

m = 12/8

m = -2

Therefore, by the given function the answer will be -2.

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The wideness of Seaside Avenue is 6.2 meters wide.

The wideness is calculated using Pythagorean theorem

Let's call the width of Seaside Avenue "x".

The description matched a right triangle where the diagonal distance is the hypotenuse and the two legs are 5 and x. The using Pythagoras theorem we have that

5² + x² = 8²

Simplifying and solving for x

x² = 8² - 5²

x² = 39

x ≈ 6.2

Therefore, Seaside Avenue is approximately 6.2 meters wide.

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Based on the given information, the capacity problem seems to be infeasible or unrealistic. This is because the resource demands (ci) for week 3, 4, and 5 are significantly higher than the available resources (ri) for those weeks. This implies that there is a problem with capacity constraints and the organization may not be able to meet the demand for those weeks.

Hi there! Based on the given data for capacity (ci) and requirements (ri) over weeks 1 to 5, the capacity problem appears feasible. Here's the comparison for each week:

Week 1: ri = 75, ci = 100 (Capacity is sufficient)
Week 2: ri = 100, ci = 200 (Capacity is sufficient)
Week 3: ri = 200, ci = 300 (Capacity is sufficient)
Week 4: ri = 100, ci = 50 (Capacity is insufficient)
Week 5: ri = 250, ci = 50 (Capacity is insufficient)

The capacity problem is feasible for weeks 1 to 3, but not for weeks 4 and 5, as the capacity is insufficient to meet the requirements in those weeks.

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Answer:

Assuming that the loan has monthly payments, the total number of payments in the 30-year loan would be 30 x 12 = 360.

To calculate how much is owed at the end of the five-year fixed period, we need to first determine how much of the principal (the borrowed amount) will be paid off during that time.

Using an amortization calculator, we can determine that with a 4.25% interest rate and monthly payments of $972.38, the principal paid off after five years will be approximately $25,732.37.

At the end of the five-year fixed period, the remaining principal balance will be $197,500 - $25,732.37 = $171,767.63. This will be the amount owed at the end of the fixed period.

Step-by-step explanation:

Answer:

x = 68°

Step-by-step explanation:

There is Two Option:

Option One: Looking at the side length we can determine that the triangle is an isosceles triangle. Which mean two angle/side are the same.

Use the Degree Angle to solve for x.

56 + 56 + x = 180

x + 112 = 180

x = 68°

Option Two: Using Law of Sine

[tex]\frac{A}{sin(A)}=\frac{B}{sin(B)} =\frac{C}{sin(C)}[/tex]

[tex]\frac{4.5}{sin(x)} =\frac{4}{sin(56)}[/tex]

[tex]sin(x)=\frac{sin(56)}{4} *4.5[/tex]

[tex]x=sin^{-1}(\frac{4.5*sin(56)}{4})[/tex]

x = 68°

The area of the shape is 89m²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The original shape is a rectangle and a triangle cut out from it.

The area of the shape = area of rectangle - area of triangle

area of rectangle = 13× 8

= 104m²

Area of the triangle = 1/2bh

= 1/2 × 5 × 6

= 5×,3

= 15m²

therefore area of the shape = 104-15 = 89m²

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The amount that the livestock market pay Ms. Horvath for the cattle is $5161.44.

The overall total of selling expenses incurred for cows totaled to $76.06 -- comprised of commission, head charge, beef promotion, and insurance costs, along with vet-testing. In order to calculate the expenditure for steers, we multiplied 0.03 with 630.17, 3 with 15, 1 with 15, and 0.00065 with 630.17; resulting in the final amount of $79.32.

For heifers, similar procedures resulted in a total cost of 64.32, attained by multiplying 0.03 with 532.44, 3 with 12, 1 with 12, and 0.00065 with 532.44.

The gross sum paid to Ms. Horvath amounted to $5,161.44 after subtracting from her cumulative sale price - 7 times 768.75, 15 times 630.17, and 12 times 532.44 - the aggregated total of the running expenditures: $219.70 (or $76.06 + $79.32 + $64.32).

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The value of c in the given function  f(x)={-x³, xc}  that makes the function f(x) continuous is calculated to be c = -1.

For the function f(x) to be continuous, it must be true that:

lim x→c- f(x) = lim x→c+ f(x) = f(c)

Let's first find lim x→c- f(x):

lim x→c- f(x) = lim x→c- (-x³) = -c³

Now, let's find lim x→c+ f(x):

lim x→c+ f(x) = lim x→c+ (xc) = c²

For f(x) to be continuous, it must be true that:

-c³ = c²

Multiplying both sides by -1, we get:

c³ = -c²

Dividing both sides by c² (note that c cannot be 0), we get:

c = -1

Therefore, the value of c that makes the function f(x) continuous is c = -1.

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The following statement is true. All other things being equal in constructing a confidence interval for a population proportion, the confidence interval constructed using a sample size of n = 500a compared to n = 200 will be a better estimate for the population proportion.

That is, the confidence interval will have a shorter length. A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence, based on a sample of data. It is commonly used in inferential statistics to estimate the range of values for a population parameter, such as a mean or proportion, based on sample data.

A confidence interval is typically represented by two values, an upper limit and a lower limit, and a confidence level, expressed as a percentage. The confidence level indicates the probability that the true population parameter falls within the interval. For example, a 95% confidence interval indicates that there is a 95% probability that the true population parameter falls within the interval.

The width of the confidence interval depends on the sample size, the variability of the data, and the chosen level of confidence. As the sample size increases, the width of the interval decreases, while increasing the level of confidence increases the width of the interval.

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Cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.

Cyclic Redundancy Checks (CRC) work as an error-detecting method used to ensure data integrity during transmission or storage. The process involves the following steps:

1. A predetermined polynomial (called the generator polynomial) is chosen for the CRC algorithm.

2. Before transmitting data, the sender divides the original data by the generator polynomial, using binary division.

3. The remainder obtained from the division is treated as the CRC value.

4. The sender appends the CRC value to the end of the original data, forming the transmitted message.

5. The receiver, upon receiving the message, performs the same binary division using the same generator polynomial.

6. If the remainder from the receiver's division matches the CRC value sent by the sender, it is assumed that the data is error-free.

7. If the remainder does not match, the receiver knows that an error occurred during transmission and can request the sender to retransmit the data.

In summary, cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.

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Answer:

6.50x+3.99

Step-by-step explanation:

every order of sweat shirts is charged 3.99

each individual sweatshirt costs 6.50 therefore x being the number purchased times 6.50 is the cost of the sweatshirts that plus the 3.99 is your total cost

Answer: y = $6x + $4.99

Step-by-step explanation:

$4.99 is only used once since you're shipping one load. There are x sweatshirts at the price of $6 each. Y is the total cost when you plug in an amount of sweatshirts for x.

hope this helps!

The  current interest rate on euro deposits is 2%, and the interest rate on dollar deposits is 3% .You should invent in d)Neither one In Europe In the US.

Using the UIP (Uncovered Interest Parity) equation, we can determine whether it is better to invest in Europe or the US. The expected future exchange rate is $1.20/€, while the current spot rate is $1.15/€. The interest rate on euro deposits is 2%, and the interest rate on dollar deposits is 3%.

The UIP equation is given by:

(Expected future exchange rate - Current spot rate) / Current spot rate = (Interest rate in domestic currency - Interest rate in foreign currency)

In this case, the domestic currency is USD and the foreign currency is EUR. Plugging in the values, we get:
($1.20 - $1.15) / $1.15 = (0.03 - 0.02)

Solving for the equation:
0.0435 ≈ 0.01

The difference in interest rates (1%) is approximately equal to the expected appreciation of the euro against the dollar (4.35%). Therefore, according to the UIP equation, there should be no significant difference between investing in Europe or the US, as the potential returns are nearly equal when considering currency movements and interest rates.

In conclusion, based on the UIP equation, you can choose to invest in either Europe or the US, as the expected returns are similar. However, it is important to consider additional factors, such as risk tolerance and investment objectives, before making a final decision. The correct answer is d.

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Answer:

301.593

Step-by-step explanation:

surface area = circumference x height + 2 x circle area

= 4 x 2 x π x 8 + 2 x π x 4^2

= 25.1327412287 x 8 + 6.28318530718 x 16

= 201.06192983 + 100.530964915

= 301.592894745 ≈ 301.593

The amount in the account after 5 years is $20202.83. Option C is correct.

Given the following parameters

Principal = $15,000

Rate r = 6% = 0.06

Time n = 5 years

The formula for finding compound interest is expressed as:

A = P(1 + r/n)^nt

A = 15,000(1 + 0.06/4)^4(5)

A = 15,000(1 + 0.015)^20
A = 15,000(1.015)^20
A = 15,000(1.3469)
A = $20202.83

Hence the amount in the account after 5 years is $20202.83

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The length of f is 11.9 ft.

We have,

d = 5.2 inches, e = 6.8 inches and ∠F=166°.

Using the law of cosines as:

f² = d² + e² - 2(de)(cos(F))

So, f² = (5.2)² + (6.8)²  - 2(5.2)(6.8)cos(166)

f² = 27.04 + 46.24 - 66.56 cos (166)

f² = 73.28 - 66.56 cos 166

f = √(73.28 - 66.56 cos 166)

f ≈ 11.9 inch.

Thus, the length of f is 11.9 ft.

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