given vectors: p= 5j, q= 2i
find: 1. p+q,
2. p-q,
3. 2p-3q

There can be 432 Types of Combinations for a 4-digit number beginning with 1 that has exactly two identical digits

What is permutation and combination?

\($11xy,\qquad 1x1y,\qquad1xy1$\)

Because the number must have exactly two identical number digits,\($x\neq y$\), \($x\neq1$, and $y\neq1$\). Hence, there are \($3\cdot9\cdot8=216$\)  number of this form.

Now suppose that the two identical digits are not 1. Reasoning similarly to before, we have the following possible combination:

\($1xxy,\qquad1xyx,\qquad1yxx.$\)

Again,,\($x\neq y$\), \($x\neq1$, and $y\neq1$\). There are \($3\cdot9\cdot8=216$\) numbers of this form.

Thus the answer is 216+216=432

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0.003 is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations

To calculate the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations.The mean is the expected number of calls involving a fax transmission, while the standard deviation is the measure of variability in the distribution. We then use this information to calculate the probability of exceeding the expected number by more than 2 standard deviations, which can be done using the z-score formula. The z-score for values more than 2 standard deviations away from the mean is 2.33, which corresponds to a probability of 0.003. Thus, the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations is 0.003.

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36 bc 20 percent of 30 is 6 so just add 6 to thirty and there you go

The solution of expression 100 divided by 8 using long division is,

⇒ 12.5

We have to given that,

100 divided by 8 using long division.

We can simplify as,

100 divided by 8 using long division as,

⇒ 100 ÷ 8

8 ) 100 ( 12.5

   - 8

 ------------

     20

   - 16

  ---------

      40

     - 40

      ------

           0

Therefore, The solution of expression 100 divided by 8 using long division is,

⇒ 12.5

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The surface area of the given figure is 215 square centimeters.

We know that the Area of a Rectangle with Length 'L and Width 'W' will be -

Area = L*W

For Rectangle II and IV, length is 5 cm and 3.5 cm.

Area of each II and IV = 5*3.5 = 17.5 square cm.

For Rectangle I and III, length is 3.5 cm and width is 15 cm.

Area of each I and III = 3.5*15 = 52.5 square cm.

Length and Width of Rectangle V are 15 cm and 5 cm respectively.

Area of Rectangle V = 15*5 = 75 square cm.

So total surface area of the figure is = (2*17.5) + (2*52.5) + 75 = 215 square cm.

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The question is incomplete. The complete question will be -

Answer:

(2,1)

Step-by-step explanation:

the best way to figure it out is with a graph

(-3,-9) to (4,5)

for the x

-3 to 4 is exactly 7 points away so you should count 5 over and stop.

for the y

-9 to 5 is exactly 14 points away so you should count in twos and stop at 5 sets of 2

hope this helps <3

Step-by-step explanation:

Hank's two cows produced a total of 43 + 22 = 65 gallons of milk.

Debra's two cows produced a total of 40 + 35 = 75 gallons of milk.

Therefore, Debra's cows produced 75 - 65 = 10 more gallons of milk than Hank's cows on that day.

Answer

y=-7

Step-by-step explanation:

The statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.

To solve the problem "La tangente de 60° es igual al triple de la tangente de 20°," follow these steps:

Step 1: Write down the equation based on the problem statement:
tan(60°) = 3 * tan(20°)

Step 2: Find the tangent values for the given angles:
tan(60°) = √3
tan(20°) = 0.36397 (approximate value)

Step 3: Plug the tangent values into the equation and check if the statement is true:
√3 = 3 * 0.36397

Step 4: Calculate the right side of the equation:
3 * 0.36397 = 1.09191 (approximate value)

Step 5: Compare the two values:
√3 ≈ 1.73205 (approximate value)

Since 1.73205 ≠ 1.09191, the statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.

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The integral \(\int_0^8 (x - x^3) dx\) does not represent the area under the curve \($y = x - x^3$\) from 0 to 8 i.e., the given statement is false.

The integral \($\int_0^8 (x - x^3) dx$\) represents the definite integral of the function \($y = x - x^3$\) over the interval [0, 8]. This integral calculates the signed area between the curve and the x-axis over that interval. However, it does not represent the area under the curve itself.

To find the area under the curve, we need to take the absolute value of the integrand.

The integrand \($x - x^3$\) can be negative for certain values of x, which would result in a negative contribution to the signed area.

By taking the absolute value of the integrand, we ensure that we only consider the magnitude of the area.

Therefore, to find the actual area under the curve \($y = x - x^3$\) from 0 to 8, we need to evaluate \($\int_0^8 |x - x^3| dx$\). This integral will give us the true area enclosed by the curve and the x-axis over the specified interval.

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we set -46λ = 0. This gives usλ = 0Thus, the value of λ such that a = 2 1 6 0 1 λ λ 0 4 is singular is `λ = 0`.

To determine the values of λ such that a = 2 1 6 0 1 λ λ 0 4 is singular we need to calculate its determinant and set it equal to zero. We can solve this by using a long answer as follows:Long Answer:We need to evaluate the determinant of the matrix `a`. The determinant of `a` is given by|a| = 2 × | 1 λ | − 1 × | 6 0 |+ 4 × | 1 λ |⇒ |a| = 2[1 × λ − λ × 0] − 1[6 × λ − 0 × 1] + 4[1 × 0 − λ × 6]|a| = 2λ − 24λ - 24λ|a| = -46λTo make the determinant zero,

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Answer:

-1/8

Step-by-step explanation:

-2³/2⁶ negative exponents go in the denonimator

-1/2³ subtract exponents since the denonimator is larger

-1/8 simplify

Answer:

Solutions below.

Step-by-step explanation:

This Question involves the concept of Function Substitution.

Function Substitution - As the name suggests, it is about substituting an input value (normally x) to find the value of y , or f(x) which is the range of the value.

Example: f(x) = 98x , f(2) = 98(2) = 196

We are given the following function:

\(p(t) = - 16 {t}^{2} + 1638\)

a) This part is asking us to find the height of the object when t = 2, which is the same as finding the value of P(2).

P(2) =

\( - 16 {(2)}^{2} + 1638 \\ = - 64 + 1638 \\ = 1574\)

Therefore at t = 2 seconds, the object is 1,574m above the river.

b) This part is asking us to find the height of the object when t = 6, which is the same as finding the value of P(6).

P(6) =

\( - 16 {(6)}^{2} + 1638 \\ = - 16(36) + 1638 \\ = - 576 + 1638 \\ = 1062\)

Therefore at t = 6 seconds, the object is 1,062m above the river.

The area bounded by the two functions f(x) = −x2 4x 2 and g(x) = −2x is =64 unit

To find the area bounded by the two functions f(x) = −x2 + 4x + 2 and g(x) = −2x + 10, we must first determine where the two functions intersect.

To do this, we set the two functions equal to each other and solve for x:

−x2 + 4x + 2 = −2x + 10
−x2 − 2x + 8 = 0
(x − 4)(x − 2) = 0
x = 4, x = 2

Now, we can calculate the area of the bounded region between f(x) and g(x):

Area = ∫24(g(x) − f(x)) dx

Area = ∫24(−2x + 10 − (−x2 + 4x + 2)) dx

Area = ∫24(x2 − 2x + 8) dx

Area = [x3/3 − x2/2 + 8x]24

Area = (64/3) − (32/2) + (64) = 64

Therefore, the area bounded by the two functions is 64.

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The frequency of heterozygous individuals in the population of piranhas can be calculated using the Hardy-Weinberg equilibrium equation. The dominant allele 'A' occurs with a frequency of 0.8, Assuming that the recessive allele 'a' occurs with a frequency of 0.2 .

According to the Hardy-Weinberg equilibrium, the frequency of heterozygous individuals (Aa) can be determined using the formula 2 xp xq, where p represents the frequency of the dominant allele and q represents the frequency of the recessive allele. In this case, p = 0.8 and q = 0.2. By substituting the values into the equation, we can calculate the frequency of heterozygous individuals as follows: Frequency of heterozygous individuals = 2 x 0.8 x0.2 = 0.32. Therefore, the frequency of heterozygous individuals in the population of piranhas is 0.32, or 32% (rounded to two decimal places). This means that approximately 32% of the individuals in the population carry both the dominant and recessive alleles, while the remaining individuals are either homozygous dominant (AA) or homozygous recessive (aa).

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Answer:

Answer 1: 0.05*0.85=0.0425

Answer 2: 0.05*0.15=0.0075

Answer 3: 0.95*0.15=0.1425

Answer 4: 0.95*0.85=0.8075

Answer 5: \(\frac{0.0425+0.0075}{0.0425+0.0075+0.1425+0.8075}=\frac{0.05}{1} =0.05=5%\)

The probability that the couple conceived a girl and the test predicts a girl is 0.0425

This refers to the branch of mathematics that has to do with the calculation of how probable an event is to occur.

To find the probability that the couple conceived a girl and the test predicts a girl is 0.05*0.85= 0.0425

The other answers are:

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Answer:

0.02777777778 or 1/36

Step-by-step explanation:

1/9 divided by 4 = 0.02777777778 or 1/36

Answer:

32

Step-by-step explanation:

The answer is 32 because 8 x 3 is 24 so then just add 8

Answer:

no because they are not like terms you can't add 2 and a variable so it would be 4k+m-2

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

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Answer:

Answer: A (97,990)

Step-by-step explanation:

135,350 (Total Assets) -  37,360 (Total Liabilities)  = 97,990

Answer:

725 x0.05=36.25

Step-by-step explanation:

when finding percentage move the decimal over two places, making 5 0.05

The expression that represents the volume of the rectangular prism, in terms of the width w, is given as follows:

6w³ cubic units.

A rectangular prism is composed by three dimensions, given as follows:

The volume of the rectangular prism is given by the multiplication of these three dimensions, as follows:

V = lwh.

From the image given at the end of the answer, the dimensions of the prism are given as follows:

Hence the expression that gives the volume of the rectangular prism is given as follows:

V = w x 2w x 3w = 6w³ cubic units.

The prism is given by the image shown at the end of the answer.

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Given:

The figure QRST.

The rule of translation is \(T_{(3,-2)}(QRST)\).

To find:

The coordinate of vertices after translation.

Solution:

According to the given rule of translation is \(T_{(3,-2)}(QRST)\), we get

\((x,y)\to (x+3,y-2)\)

From the given figure it is clear that the vertices of QRST are Q(1,3), R(3,-3), S(0,-2) and T(-2,1).

Using the above rule, we get

\(Q(1,3)\to Q'(1+3,3-2)=Q'(4,1)\)

\(R(3,-3)\to R'(3+3,-3-2)=R'(6,-5)\)

\(S(0,-2)\to S'(0+3,-2-2)=S'(3,-4)\)

\(T(-2,1)\to T'(-2+3,1-2)=T'(1,-1)\)

Therefore, the coordinates of the vertices after translation are Q'(4,1), R'(6,-5), S'(3,-4) and T'(1,-1).

The ordered pairs for the vertices of T(3, –2)(QRST) are

\(\mathbf{Q' = (4,1)}\)  \(\mathbf{R' = (6,-5)}\)  \(\mathbf{S' = (3,-4)}\) and \(\mathbf{T' = (1, -1)}\)

The coordinates of QRST are:

\(\mathbf{Q = (1,3)}\)

\(\mathbf{R = (3,-3)}\)

\(\mathbf{S = (0,-2)}\)

\(\mathbf{T = (-2,1)}\)

The transformation rule of \(\mathbf{T(3,-2)}\) is:

\(\mathbf{(x,y) \to (x + 3,y -2)}\)

So, we have:

\(\mathbf{Q' = (1 + 3,3 -2)}\)

\(\mathbf{Q' = (4,1)}\)

\(\mathbf{R' = (3 + 3,-3 -2)}\)

\(\mathbf{R' = (6,-5)}\)

\(\mathbf{S' = (0 + 3,-2 -2)}\)

\(\mathbf{S' = (3,-4)}\)

\(\mathbf{T' = (-2 + 3,1 -2)}\)

\(\mathbf{T' = (1, -1)}\)

Hence, the ordered pairs for the vertices of T(3, –2)(QRST) are

\(\mathbf{Q' = (4,1)}\)  \(\mathbf{R' = (6,-5)}\)  \(\mathbf{S' = (3,-4)}\) and \(\mathbf{T' = (1, -1)}\)

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Why do we include 40 if it says less than?

Good question.

We include 40 because it technically counts as representing itself or anything within the range of 20 and 40

Answer:

a=7 b=14

Step-by-step explanation:

I left an attachment for how I solved it

The mean of the fitted exponential distribution is 66.67.

To find the mean of the fitted exponential distribution, we first need to estimate the parameter lambda using maximum likelihood estimation.

The probability density function of the exponential distribution is given by

f(x; lambda) = lambda * exp(-lambda * x)

where x is the claim size and lambda is the parameter to be estimated.

The likelihood function for the observed data is the product of the individual probabilities of each claim

L(lambda) = lambda^n * exp(-lambda * sum(x_i))

where n is the number of observed claims and x_i is the i-th claim size.

The log-likelihood function is given by:

ln L(lambda) = n * ln(lambda) - lambda * sum(x_i)

To estimate the parameter lambda, we need to maximize the log-likelihood function with respect to lambda:

d/d(lambda) ln L(lambda) = n/lambda - sum(x_i) = 0

Solving for lambda, we get

lambda = n / sum(x_i)

Substituting the observed values, we get

lambda = 6 / (20 + 45 + 50 + 80 + 100 + 2*100) = 0.015

Therefore, the estimated parameter of the fitted exponential distribution is lambda = 0.015.

The mean of the exponential distribution is given by

E(X) = 1/lambda

Substituting the estimated value of lambda, we get

E(X) = 1/0.015 = 66.67

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Answer:

34

Step-by-step explanation:

you first write the equation:

(8-3) / (8+x-7) = 1/7, where x is the number of non blue socks

so, 5/(1+x) = 1/7

1+x = 35, so x=34

The ladder needs to be 34.3m long from tree you to get to get the cat.

We must determine the hypotenuse in this right triangle, which is the side that is opposite the triangle's 90° angle. When the neighboring side is 23 meters away, the elevation angle is  54°

Suppose Hypotenuse equals h.

Given, the base is 23m

Using trigonometry,

tan θ = Base / hypotenuse

tan 54° = 23 / h

⇒ 0.67 = 23 / h

⇒ h = 23 / 0.67

⇒ h = 34.3

So, the ladder needs to be 34.3m away in order to reach cat.

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