tony received 80 dollars for his birthday. He went to a sporting goods store and bought a baseball glove, baseball, and bat. He had 38 dollars left over, how much did he spend on the baseball gear ?

From the counting principal, the possible formed distinct 3 digit numbers from the digits 1,2,3,4 with repititions is equals to the 64 ways.

W have a total number of digits = 4 = {1,2,3,4}

We have to form three digit number with repetition.

The unit’s place can be filled by any of the four digits. Since, the repetition of the digits is allowed, thus, the remaining two places that are ten’s and hundred’s places can also be filled by any of the four digits. So, the number of ways in which the three-digit numbers can be formed from these digits can be calculated by multiplication principle which states that if an event can occur in m different ways and follows another event that can occur in n different ways, then the total number of occurrence of the events in the order is m×n. Since, each place have 4 ways to obtain any of digit.

The total number of ways to form three digit numbers with repetition is = 4³ = 64

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The range of the function y = 2sin(x) is the set of all possible values that the function can take. The range of the function y = 2sin(x) is [-2, 2].

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function, sin(x), has a range between -1 and 1, inclusive. When we multiply the sine function by 2, as in the case of y = 2sin(x), the range is expanded.

Multiplying the range of sin(x) [-1, 1] by 2 gives us the range of 2sin(x), which is [-2, 2].

Therefore, the range of the function y = 2sin(x) is [-2, 2].

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Answer:

\(\boxed{\bf \angle A=84^o}\)

Step-by-step explanation:

From the given diagram, we can see that ∠B & ∠C are corresponding angles, which means that they are equal. The two angles that form a straight line are supplementary angles (the sum of two supplementary angles is 180°).

\(\bf 5x+34^o+\angle C=180^o\)

\(\bf 5x+34^o+\angle B=180^o\)

\(\bf 5x+34^o+2x+76^o=180^o\)

Now, let's solve for x :-

\(\bf (5x+34^o)+(2x+76^o)=180^o\)

\(\bf (5x+2x)+(34+76)=180^o\)

\(\bf 7x+110=180^o\)

\(\bf (7x+110)-110^o=180-110^o\)

\(\bf 7x=70^o\)

\(\bf \cfrac{7x}{7} =\cfrac{70}{7}\)

\(\boxed{\bf x=10^o}\)

Now, in order to find ∠A will substitute the value of x  into the expression:-\(\bf \angle A=5x+34^o\)

\(\bf \angle A=5(10)+34^o\)

\(\bf \angle A=84^o\)

______________________

Answer: 54 Coins are not nickel( 16+14+24)

n= 74 - non nickel

n= 74- (penny+ dime+ quarter)

n= 74- (16+14+24)

Step-by-step explanation:

Answer:

because, for any n by n matrix, the sum of the dimension of the column space and the dimension of the null space must equal n. If the two dimensions are the same, their sum is an even number.

Step-by-step explanation:

It is impossible for an n-by-n matrix, where n is odd, to have a null space equal to its column space because the dimensions of the two spaces cannot be the same.

The null space of a matrix A is the set of all solutions to the equation Ax=0, where x is a column vector of appropriate dimensions. The column space of A is the span of the columns of A, which is the set of all linear combinations of the columns of A.

If the null space and column space of A are equal, then the dimension of the null space must be equal to the dimension of the column space. By the Rank-Nullity Theorem, the sum of the dimensions of the null space and the column space is equal to the number of columns in A.

Therefore, if n is odd, the dimensions of the null space and column space cannot be equal since their sum is even. Therefore, it is impossible for an n-by-n matrix, where n is odd, to have a null space equal to its column space.

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Answer:

The newspaper has 1,600 readers.

Answer:

-7/4

Step-by-step explanation:

(-1,2) (3,-5)

x1 y1 x2 y2

-5-2=-7

3-(-1)=4

-7/4

Answer:

for this graph the answer is D

Answer:

True

Step-by-step explanation:

The answer is 4 runners. You translate the fractions to real numbers, 3/4 is 0.75 and 3/16 is .1875 & u simply divide .75 by .1875 and you get 4.

Answer:

4 runners

Step-by-step explanation:

Total cover = 3/4

Reciprocal the 3/16 will become 16/3 then Multiply 3/4 = 0.75 times 16/3  = 5.33 by multiplying numerator times numerator and denominator times denominator.

3 x 16 = 48

4 x 3 = 12

Overall it is 48/12

48/12 is an improper fraction it can change into a whole number

48/12 = 4

Answer:

B. \( 6 \frac{9}{16} \) (second option)

Step-by-step explanation:

\(8 - 1 \frac{7}{16} \\ \\ \frac{1 \times 16 + 7}{16} = \frac{16 + 7}{16} = \frac{23}{16} \\ 8 - \frac{23}{16} = \frac{128 - 23}{16} = \frac{105}{16} \)

\( \boxed{Answer:{\boxed{\green{= 6 \frac{9}{16}}}}} \)

hope that helped

The coin purse hit the ground in 3 seconds.

Given :

\($\mathrm{f}(\mathrm{t})=16 \mathrm{t}^2$\) ----- (represent the distance(in feet) a dropped object falls in t seconds)

\($\mathrm{g}(\mathrm{t})=\mathrm{s}_0=144 \mathrm{ft}$\) ------ (represent the initial height (in feet) of the coin purse)

The function that represents the distance a dropped coin purse falls in t seconds,

\($f(t)=144-16 t^2$\)

When the coin purse touches the ground,

\($f(t)=0$\)

\($0=144-16 t^2$\)

\($t^2=\frac{144}{16}=9$\)

t = +3 and t = -3

So we take positive t.

Therefore, the coin purse hit the ground in 3 seconds.

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Answer:

Step-by-step explanation:

Given ratio of boys and girls in the class =7:5

No of boys is 8more than the girls

So

Let no of boys in the class =7x

No of girls in the class=5x

7x=5x+8

2x=8

X=8/2

X=4.

Total strength =no of boys + no of girls

=7x+5x

=7×4+5×4

= 28+20

=48.

Total strength in the class is 48.

Answer:

Total class strength = 48

Step-by-step explanation:

Boys : Girls = 7 : 5

Number of boys  = 7x

Number of girls = 5x

7x - 5x = 8

      2x = 8      

       x = 8/2

       x = 4

Total strength = 7x + 5x = 12x = 12*4  = 48

The number of ways that there are for her to plan her schedule of menus for the 20 school days, with no restrictions, using the Fundamental Counting Theorem, is of:

10^20.

The Fundamental Counting Theorem states that if there are n independent trials, each with \(n_1, n_2, \cdots, n_n\) possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

In this problem, we have that:

Then the number of different meals is obtained as follows:

N = 10^20.

As there are 20 trials, each with 10 possible outcomes.

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By examining the pattern of correlations between multiple traits and methods, we must identify method effects using the MTMM matrix.

The MTMM matrix is a matrix of correlations that compares the inter-correlations between multiple traits (variables) and multiple methods used to measure those traits.

To identify method effects using the MTMM matrix, we need to look at the pattern of correlations between the traits and methods. Specifically, we are interested in the pattern of correlations where the same trait is measured using different methods.

Additionally, we can also examine the pattern of correlations between different traits measured with the same method. If the correlations between different traits measured with the same method are high, this suggests that the method is reliable and valid.

However, if the correlations are low, this may indicate that the method is not accurately measuring the traits, or that there are other factors (e.g., method effects) influencing the results.

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Answer:

(3, 1)

Explanation:

because that's where they intercept

Answer:

Both lines intersects at (3, 1)

given:

solve them simultaneously:

solve for y:

Answer:

each song would be 67 cents (0.67)

Step-by-step explanation:

9.38/14=0.67

Answer:

19.2 your welcome my guy

Step-by-step explanation:

im smart

Yeah your not the only one i am to

The expressions that have 3 as the greatest common factor are b + 3 + 6c, 27n + 66p, and 36 - 9j + 6k.

Thus,

b + 3 + 6c         - Yes

-30 - 24z           - No

27n + 66p         - Yes

36 - 9j + 6k       - Yes

From the question, we are to determine if 3 is the greatest common factor of the given expressions

b + 3 + 6c

3(b + 1 + 2c)

The greatest common factor is 3

-30 - 24z

6(-5 -4z)

The greatest common factor is not 3. The greatest common factor is 6

27n + 66p

3(9n + 22p)

The greatest common factor is 3

36 - 9j + 6k

3(12 - 3j + 2k)

Thus, The greatest common factor is 3

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Answer:

7.171428571

Step-by-step explanation:

<3

This statement is true because both 5 is a whole number and 3 is a positive number, satisfying at least one of the conditions.

Let's go through each statement and answer the questions:

Statement 1: (30 out to the movie).

This is not a proposition because it is not a complete statement. It lacks a clear subject or predicate.

Statement 2: Where did the cat go?

This is not a proposition because it is a question and not a declarative statement.

Statement 3: There is a chipmunk in the backyard.

This is a proposition because it is a complete statement making a claim about the presence of a chipmunk in the backyard.

Statement 4: 15 - 22 = 100.

This is a proposition, but it is a false statement since 15 - 22 is not equal to 100.

Question 2: Assuming p is True and q is False.

We need a specific statement or proposition to evaluate its truth value using the given truth values of p and q.

Question 4: 5 is an odd number and 6 is a prime number.

This statement is false because 6 is not a prime number. It is divisible by 2 and 3, making it composite.

Question 5: 8 is an odd number or 7 is a prime number.

This statement is true because 8 is an odd number, satisfying the first condition.

Question 6: 5 is a whole number or 3 is a positive number.

This statement is true because both 5 is a whole number and 3 is a positive number, satisfying at least one of the conditions.

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Perform orthogonal transformation to eliminate cross-product terms in quadratic form.

Perform an orthogonal transformation to convert the quadratic form into one with no cross-product terms.

Given the quadratic form x'Ax, determine if it is positive definite and if matrix A is idempotent.

Explain why the product of a random variable y and a symmetric idempotent matrix M is not a chi-square variable.

State an assumption needed for y'Ay and y'By to be independent, where y is a random variable and A and B are idempotent matrices.

Show that the quadratic form X'AX follows a chi-square distribution with degrees of freedom (r,0) using the properties of idempotent matrices and the distribution of a vector Z.

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By answering the above question, we may state that we have assumed equation that the prerequisites for inference using a confidence interval have been satisfied.

A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.  

Sample Size: The sample size should be large enough to guarantee that the mean sampling distribution is roughly normal. There is no hard and fast rule regarding what makes a "big enough" sample size, although a sample size of at least 30 is regarded sufficient. The sample size for both men and women is fewer than 30 in this situation.

We may proceed with generating a 95% confidence interval to estimate the difference between men and women in the mean number of days for the duration of stay at a hospital since we have assumed that the prerequisites for inference using a confidence interval have been satisfied.

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Answer:

x = 6 when f(x)=20

Step-by-step explanation:

\(f(x)=2(x+4)\\f(x)=2x+8\\\\20=2x+8\\12=2x\\6=x\)

The shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

It is given that:

The equation of the line is:

y = 2x + 4

Or

2x - y + 4 = 0

The point is (0, 0)

As we know, the formula for the shortest distance between the line and a point:

D = |ax + bx + c|/√(a²+b²)

Plug x = 0 and y = 0

a = 2, b = -1, and c = 4

D = |2(0) + -1(0) + 4|/√(2²+(-1)²)

D = 4/√5

D = 1,78 ≈ 1.8 units

Thus, the shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.

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Answer:

$150

Step-by-step explanation:

100/8=12.5

12.5*12=150

Answer:

(800 x 9) + (10 x 9)

Step-by-step explanation:

Find out what 810 x 9 is:

810 x 9 = 7290

Then see which expression has the same answer. Personally I'd check all of them, but luckily the first expression is the correct one so you don't need to go through the rest (since it only asks for one correct expression):

(800 x 9) = 7200

(10 x 9) = 90

7200 + 90 = 7290

The variable associated with the interior and exterior angles in the triangle is equal to 56.

The value of the exterior angle is equal to 116°.

This question presents the case of a geometric system formed by a triangle and a semirray that includes two interior angles and a exterior angle. Please notice that the sum of the measures of interior angles in a triangle equals 180° and the sum of two supplementary angles equals 180°.

First, derive the equation of the missing interior angles in triangle PQR:

m ∠ R = 180° - 60° - x

m ∠ R = 120° - x

Second, obtain the equation for the two supplementary angles:

(120° - x) + (2 · x + 4°) = 180°

124° + x = 180°

x = 56

Third, determine the value of the exterior angle:

θ = 2 · x + 4

θ = 2 · 56 + 4

θ = 116°

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