Translate the sentence into an inequality.
A number b increased by 9 is less than -22.

Using the trigonometric symmetries we can rewrite  the expression in terms of sin(z) as:  

\(\[\frac{1}{{\sqrt{{1 - \sin^2(z)}}}} + \frac{1}{{\sin(z)}}\]\)

Let's complete the identities using the trigonometric symmetries from the table:

a. sin(-a) = -sin(a) (Using the symmetry: sin(-a) = -sin(a))

b. cos(-x) = cos(x) (Using the symmetry: cos(-x) = cos(x))

c. tan(-2) = -tan(2) (Using the symmetry: tan(-x) = -tan(x))

Now, let's rewrite the expression in terms of sin(z):

\(\sec(z) + \csc(z) = \frac{1}{\cos(z)} + \frac{1}{\sin(z)}\)

To rewrite this expression in terms of sin(z), we can use the identity:

\(\[\sec(z) = \frac{1}{\cos(z)} = \frac{1}{\sqrt{1 - \sin^2(z)}}\]\csc(z) = \frac{1}{\sin(z)}\]\)

So, the expression becomes:

\(\[\frac{1}{{\sqrt{{1 - \sin^2(z)}}}} + \frac{1}{{\sin(z)}}\]\)

This is the rewritten expression in terms of sin(z).

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So, the two factors of 16 that have a product of 16 and a sum of 10 are 8 and 2.

The first number is 16 and the second number is 10. We need to find two factors of 16 such that their product is 16 and their sum is 10.

Let's start by listing the factors of 16:

1, 2, 4, 8, 16

To find two factors that satisfy the given conditions, we can start with the largest factor (16) and work our way down, looking for a pair of factors whose sum is 10.

16 + 1 = 17

16 + 2 = 18

16 + 4 = 20

16 + 8 = 24

16 + 16 = 32

None of these pairs of factors add up to 10, so we need to move on to the next largest factor, which is 8.

8 + 1 = 9

8 + 2 = 10

We have found a pair of factors whose sum is 10, so we can check if their product is 16:

8 x 2 = 16

So, the two factors of 16 that have a product of 16 and a sum of 10 are 8 and 2.

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Answer:

52kg

Step-by-step explanation:

If you put the numbers in order from least to greatest you get:

43, 48, 52, 59, 63. The median is the one in the middle. So you get 52 is the median

Answer:

Hey here's ur answer

Step-by-step explanation:

Hope it helps

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

The constant of proportionality is 10 in the given graph which represents the total number of plants and number of seed packets used.

Equivalence between two ratios is referred to as proportionality in algebra. A and B are in the same proportion as C and D in the expression a/b = c/d. When one of a proportion's four quantities is unknown, a proportion is typically used to solve a word problem.

It is resolved by multiplying one numerator by the opposing denominator and equating the result to that of the other numerator and denominator. Any relationship that always has the same ratio is referred to as proportional.

For instance, the ratio of proportionality is the average number of apples per tree, and the quantity of apples in a crop is proportional to the number of trees in the orchard.

Here, when number of seeds packet is 1 plants are 10 and when seeds packet are 5 plants are 50, we can divide each of the variables to find the constant,

10/1 = 10

20/2 = 10

30/3 = 10

Thus, constant is 10 represented as y = kx

where y = no. of plants = 30

k = 10

x = no. of seeds packet = 3

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Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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Answer:

no its 1749

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

(a)

To multiply two polynomials, multiply every term of the first polynomial by every term of the second polynomial. Then combine like terms.

\( (\dfrac{1}{2}x - \dfrac{1}{4})(5x^2 - 2x + 6) = \)

\( = \dfrac{1}{2}x \times 5x^2 - \dfrac{1}{2}x \times 2x + \dfrac{1}{2}x \times 6 - \dfrac{1}{4} \times 5x^2 + \dfrac{1}{4} \times 2x - \dfrac{1}{4} \times 6 \)

\(= \dfrac{5}{2}x^3 - x^2 + 3x - \dfrac{5}{4}x^2 + \dfrac{1}{2}x - \dfrac{3}{2}\)

\( = \dfrac{5}{2}x^3 - \dfrac{9}{4}x^2 + \dfrac{7}{2}x - \dfrac{3}{2} \)

(b)

No. Since the binomials are different, the product of two different binomials and the same trinomial will give different results.

the given triangles are not similar

so they will not be congruent

so the answer is not similar

The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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use the calculator but the answer is 18.1

the correct answer is option a: 10/3, which represents the mean and standard deviation of the scaled scores on the WISC-V.

Scaled scores are used to compare an individual's performance on the WISC-V to the performance of other individuals in the same age group. The scaled scores are derived from raw scores and are standardized to have a mean and standard deviation that are predetermined.The mean of scaled scores on the WISC-V is set to 10. This means that an average performance is represented by a scaled score of 10.

The standard deviation of scaled scores on the WISC-V is set to 3. The standard deviation measures the spread or variability of scores around the mean. A standard deviation of 3 indicates that most scores fall within 3 points above or below the mean of 10.

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Answer:

Step-by-step explanation:

f(x) = - x + 6

g(x) = 4x - 6

In order to find g(f(x)) substitute f(x) into g(x) that's for every x in g(x) replace it with f(x)

That's

We have the final answer as

Hope this helps you

Answer:

2 \(\frac{1}{2}\)pizzas

Step-by-step explanation:

The equation to this question can be written as 5/6 + 5/6 + 5/6 or 5/6 x 3.

To multiply 5/6 by 3, we can set it up as \(\frac{5}{6} * \frac{3}{1}\). Now to multiple, we just multiply straight across. We do 5 * 3 over 6 * 1 to get 15/6. Now, all we have to do is simplify the fraction. 6 goes into 15 two times, so we know they ate 2 pizzas. Now we are left with 3/6. 3/6 can be rewritten as \(\frac{1}{2}\). In total, they ate 2 \(\frac{1}{2}\) pizzas.

Hope this helps!

Answer:

B) the slope is -10 and the y-intercept is +1

Step-by-step explanation:

The lope comes before the x, and the y-intercept comes after the x. Hope this helps.

Answer:

the answer is B

Step-by-step explanation:

i did the math QUIZ 8th grade EDG

Answer:

Step-by-step explanation:

Answer: 160 m^2.

Step-by-step explanation:

Answer: 2 minutes

Step-by-step explanation:

Given the following :

Plane A's descent :

y = -2,500x + 14,000

Plane B's Ascent :

y = 4,000x + 1,000

where y = altitude x = minute

Time to be at the same altitude :

Being at the same altitude means ;

Plane A's descent = Plane B's Ascent

-2,500x + 14,000 = 4,000x + 1,000

-2500x - 4000x = 1000 - 14000

-6500x = - 13000

x = 13000 / 6500

x = 2

x = 2minutes.

Do you know the adjustments for the graph to show the intersecting lines.

Answer:

1.Understand the problem

2.Gather your resources

3.Come to answer

4.Check your answer and present solution

Step-by-step explanation:

Answer:

Number 1 is gather your resources

Number 2 is understand the problem

Number 3 is come to an answer

and number 4 is check your answer and present the solution

Identify the predictor and response variables, then create a scatterplot in Minitab. Characterize the association between the variables as linear or nonlinear and negative, none, or positive.

In exploratory data analysis, the first step is to identify the research question and the two variables of interest. The predictor variable (also known as the explanatory variable or independent variable) is the one that is used to explain or predict the outcome of the response variable (also known as the dependent variable).

After identifying the two variables, one can use software such as Minitab to create a scatterplot of the data. The scatterplot helps to visualize the relationship between the two variables.

To characterize the association between the two variables, we would first determine if the relationship appears to be linear or nonlinear. If the relationship is roughly linear, we would then determine if it is negative (meaning that as one variable increases, the other tends to decrease), positive (meaning that as one variable increases, the other tends to increase), or none (meaning that there is no clear trend).

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Based on the information provided, the archaeological sample's estimated age is = 0.214136  years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 23 % of the 14C remains

then |A1|/|A2|  = 0.23

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.23)= -1.46967

t = -0.31471/ --1.46967

= 0.214136 years

The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay).

The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite life's in exponential growth is time's doubling.

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Answer: x=3.2

Ste by Step

We have that for the Question "The figures are similar, and the ratio of the perimeters is 2 : 5. Find x." it can be said that  the perimeters of x is

x=3.2

From the question we are told

The figures are similar, and the ratio of the perimeters is 2 : 5. Find x.

Generally the equation for the the ratio is mathematically given as

2=x

and

5=8

Therefore

x=3.2

Therefore

the perimeters of x is

x=3.2

Answer:

Discrete

Step-by-step explanation:

Given the function:

f(x) = 100x + 300

Where ;

x = number of attendees

At least 4 students but no more than 9 students will attend the fieldtrip due to transportation and chaperone restrictions

Range of attendees :

4 ≤ x ≤ 9

Is this a discrete or continuous situation?

It is a discrete because the number of students who will attend the science weekend are finite and countable.

The number of attendees range from:

4, 5, 6, 7, 8 and 9.

Answer:

x=7,x=-1/2

Step-by-step explanation:

so x-7=0 or 2x+1=0

x=7 or 2x=-1

x=7,x=-1/2

if my answer helps please mark as brainliest.

Given:

The perimeter of a square is 54cm.

To find:

The length of a diagonal, rounding to the nearest tenth. ​

Solution:

Let a be the length of each side of square.

We know that, perimeter of a square is

\(Perimeter = 4a\)

\(4a=54\)

Divide both sides by 4.

\(a=\dfrac{54}{4}\)

\(a=13.5\)

We know that, diagonal of a square is

\(d=\sqrt{2}a\)

\(d=(1.414)(13.5)\)

\(d=19.089\)

Rounding to the nearest tenth, we get

\(d\approx 19.1\)

Therefore, the length of diagonal is about 19.1 cm.

Answer:

You are correct great job! I believe you did

1/4 × 1/9 = 1/36 If so thats exactly the right method!

The investment's expected return is 5.95%.

The expected return of an investment is calculated by multiplying the probabilities of each possible return by their respective returns and summing them up. In this case, Gautney Enterprises has provided the probabilities and returns for the investment. By applying the formula, we find that the expected return is 5.95%.

To calculate the standard deviation, we need to determine the variance first. The variance is computed by taking the difference between each possible return and the expected return, squaring those differences, multiplying them by their respective probabilities, and summing them up. Once we have the variance, the standard deviation is simply the square root of the variance. The standard deviation measures the degree of risk associated with an investment.

In this scenario, the expected return of the investment is 5.95%, but we need to consider the standard deviation as well to assess the risk. If the standard deviation is high, it indicates a greater level of uncertainty and potential volatility in returns. A low standard deviation implies a more stable investment.

Without the specific values for each return and their respective probabilities, we cannot calculate the exact standard deviation. However, Gautney Enterprises should compare the calculated expected return and the associated standard deviation to their risk tolerance and investment objectives. If the expected return meets their desired level of return and the standard deviation aligns with their risk appetite, they may consider investing in this security.

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