Suppose that the functions and are defined for all real numbers x as follows.

s(x) = 4x
t(x) = 3x + 3


Write the expressions for
(t*s)(x)
(t - s)(x)
and evaluate (t + s)(- 2)

The following system of equations has no solutions, the correct option is A.

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

We have given that;

system of equations are

x+y=-4.....1

-x-y=4......2

Now,

Rearranging the equation 2

-4=x+y

Its equal to equation 1

Therefore, the system of equations will have no solution.

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The perimeter of the figure is 30.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure,

Number of sides = 5

Each side = 6

So,

The perimeter.

= 5 x 6

= 30

Thus,

30 is the perimeter.

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Answer:

x = 59.036°

Step-by-step explanation:

tan (BÂC) = BC/AB

tan= opposite/ adjacent

Then subs AB = 3 BC= 5 BÂC= x into tan (BÂC) = BC/AB

tan(x)=5/3

x= tan^-1 (5/3)

x= 59.036°

Final Answer:

There are 0.036 decimeters in 3.6 millimeters.

Explanation:
To convert from millimeters to decimeters, we can use the following measurement conversion:

1 millimeter = 0.01 decimeters

So, to find out how many decimeters are in 3.6 millimeters, we can multiply 3.6 by 0.01:

3.6 * 0.01 = 0.036

Therefore, there are 0.036 decimeters in 3.6 millimeters.

Peter the rabbit have  51 carrots are left.

one fourth means A quarter is represented in mathematics using fractions. Mathematically, a quarter fraction is a whole divided into four equal parts. where 1 indicates the part being referenced and 4 indicates the number of parts the whole is divided into. In numeric format, it is written as ¼.

so total carrot is 84

and he ate one fourth on that day

so remaining are

84*1/4= 21

21 he eat on that the then remaining =

84 - 21  = 63

63 carrots are remain for next day and

he eat 12 carrot on next day

so remaining = 63 - 12 = 51

so 51 carrot left .

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Answer:

It would be 180 - 136 = 44

Step-by-step explanation:

Answer:

yes you are correct

Step-by-step explanation:

180-136=44

Answer:

ray ts

Step-by-step explanation:

Range, interquartile range, standard deviation, and variance are four measures of variability that can be used to compare two data sets.

area:

Difference between highest and lowest values.

Range is the straightforward allowance to calculate variability. To asset the area, follow these steps:

Sort all the values ​​in the dataset from lowest to highest.

Subtract the lowest value from the highest value. Interquartile range:

area of ​​the middle half of the distribution

standard deviation:

mean distance from mean

Standard deviation is a useful measure of the variance of a normal distribution.

A normal distribution distributes data symmetrically without skew. Most of the values ​​are clustered around the central region, with values ​​tapering away from the center. Standard deviation indicates how far the data are, on average, from the center of the distribution.

deviation:

mean squared distance from mean 

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A manufacturer working at the 430 gram setting, and a 21 bag sample had a mean of 421 grams with a standard deviation of 15. The p-value of test statistic is 0.0074.

To test whether the bag filling machine works correctly at the 430 gram setting, we can conduct a one-sample t-test. The null hypothesis is that the true mean weight of the bags filled by the machine is equal to 430 grams, and the alternative hypothesis is that the true mean weight is less than 430 grams.

The test statistic is calculated as:

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

Plugging in the values given in the problem, we get:

t = (421 - 430) / (15 / sqrt(21)) = -2.77

The degrees of freedom for the t-distribution are n - 1 = 20.

Using a t-table or calculator, we can find the p-value associated with a t-score of -2.77 and 20 degrees of freedom. The p-value turns out to be 0.0074 (rounded to four decimal places).

Since the p-value is less than the level of significance of 0.1, we can reject the null hypothesis and conclude that the bag filling machine is underfilling the bags at the 430 gram setting.

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how will his speed compare?  or namely, will he be within speed limits or should we give him a big fat ticket for speeding?

well, the 25 mi/hr limit is expecting anyone on that road to only do 40,234 meters per hour, so since an hour is 60 minutes and a minute is 60 seconds, that means an hour is really (60)(60) seconds, or 3600 seconds, so the limit is expecting anyone on that road to do no more than 40,234 meters per 3600 seconds, let's see how Usain fares

[tex]\begin{array}{ccll} meters&seconds\\ \cline{1-2} 100 & 9.63\\ 40234& x \end{array} \implies \cfrac{100}{40234}~~=~~\cfrac{9.63}{x} \implies 100x=(40234)(9.63) \\\\\\ x=\cfrac{(40234)(9.63)}{100}\implies x\approx 3874.53[/tex]

so Usain will covering those 40,234 meters in about 3875 seconds, that's longer than 3600 seconds, meaning Usain will need more than 3600 seconds to cover those meters so he's really going slower 40,234 meters per 3600 seconds, so he's golden,  he's within speed limits, because the limit is expecting noone to do them in less than 3600 seconds.

Answer:

to help navigate the answer

The appropriate option to fill the blanks would be: a. validity. and b. reliability.

Both validity and reliability are important concepts in research that determine the quality of data and measurement. Validity refers to the accuracy and truthfulness of a measurement, while reliability refers to the consistency and stability of a measurement. The researcher would be interested in both to ensure that the data measure what they are supposed to measure accurately and consistently. In research, both reliability and validity are important concepts. Reliability refers to the consistency and stability of a measurement, while validity refers to the accuracy and truthfulness of a measurement. So, if a researcher wishes to examine the extent to which the data measure what they are supposed to measure, the researcher would be interested in both reliability and validity of the data.

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Complete Question

If a researcher wishes to examine the extent to which the data measure what they are supposed to measure, the researcher is interested in _________

a. validity.

b. reliability.

c. confirmability.

d. credibility.

Answer:

y- intercept = 4

Step-by-step explanation:

the y- intercept is the value of y on the y- axis where the line crosses.

the line crosses the y- axis at 4

then y- intercept = 4

The cost of red grapes per pound is $2.8.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, cost of a large watermelon and 2.4 pounds of red grapes is $7.71.

Let the cost of red grapes be x.

So, the total cost = 7.71+2.4x

Cost of a platter of pre-cut fruit and 1.6 pounds of red grapes is $9.95.

The total cost = 9.95+1.6x

Person and his brother spent same amount of money.

So, 7.71+2.4x=9.95+1.6x

2.4x-1.6x=9.95-7.71

0.8x=2.24

x=2.24/0.8

x=$2.8

Therefore, the grapes cost per pound is $2.8.

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The value of x by using the addition postulate of an acute angle is 36.

Acute angles are those between 0 and 90 degrees, and those angles are less than 90 degrees. When two rays intersect at a vertex, an angle is created.

An acute angle is one that is smaller than 90 degrees in length and has all internal angles that are less than 90 degrees.

Here, we have an acute angle NCQ that is 70 degrees. Using the addition postulate to determine the value of x, we have:

x + 34 = 70

x = 70 + (-34)

x = 70 - 34

x = 36

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the probability of getting (a, b), i.e. the first card is a and the second card is b is 2/3 by conditional probability.

The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is computed by dividing the likelihood of the earlier occurrence by the likelihood of the subsequent, or conditional, event.

This is where the independent event and dependent event notion is used. Consider a student who misses class twice each week, omitting Sunday. What are the possibilities that he will take a leave of absence on Saturday of the same week if it is known that he will be absent from school on Tuesday? It has been noted that situations where the outcome of one event influences the outcome of a subsequent event are termed as conditional probability

We can work this out directly from the definition of conditional probability,

[tex]P(G_1|G_2)=P(G_1nG_2)/(P(G_1)[/tex]

Exactly one of the three cards has sides, so

P(G1∩G2)=1/3

and P(G1)=1/2

THEN

the probability of getting (a, b), i.e. the first card is a and the second card is b IS = 1/3÷1/2 = 2/3

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The dot product a . b is -22

The dot product, also known as scalar product or inner product, is a binary operation that takes two vectors and returns a scalar (single-valued) quantity. The dot product of two vectors is equal to the product of the magnitude (length) of the vectors and the cosine of the angle between them.

Given two vectors, A and B, the dot product is defined as:

A ∙ B = |A| * |B| * cos(θ)

where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.

a = <3, -2>

b = <-2, 8>

a . b = (3 * -2) + (-2 * 8)

a . b = -6 + - 16

a . b = -22

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Answer:

4 and -2

Step-by-step explanation:

4 + -2 = 2

4 x -2 = -8

The true statement about JK and JL is, JK is longer than JL

The process of comparison reveals the shared characteristics of several objects. This is the fundamental idea in mathematics that guides our descriptions of whether two numbers are equal, one is more than, one is less than, or both are equal. Comparing fractions, decimals, and rational numbers are all possible.

The coordinates of the point are:

J (2, 4)

K (7, 8)

L (1, -1)

The distance between two points is given by the formula:

D = √(x2 - x1)² + (y2 - y1)²

The distance between JK is:

JK = √(7 - 2)² + (8 - 4)

JK = √25 + 16 = √41 = 6.40

The distance between JL is:

JL = √(1 - 2)² + (-1 - 4)²

JL = √1 + 25 = √26 = 5.09

Hence, the statement about JK and JL is, JK is longer than JL.

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The complete question is:

The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is 5/52

probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations.

Given that, if each coded item in a catalog begins with 4 distinct letters followed by 4 distinct nonzero digits

Like the 4 distinct letters be A,B,C,D

4 distinct nonzero digits are 2,3,4,5

The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to the 10/104 = 5/52

Here the probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations and the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to 5/52

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Answer: 28

Step-by-step explanation:

16% = 0.16

Percents are just decimals!

Now you can put this in your calculator, and you will get 28.

However:

It might help you later to know that x% of y = y% of x

In other words, 16% of 175 is the same thing as 175% of 16

This problem is easier, since we can break 175% into 1 and 3/4th. 3/4th of 16 is easy to calculate, (its 12), and so we can add 12 to 16 to find the answer, which is still 28 :)

No calculator needed!

Answer: 52 Degrees

Step-by-step explanation:

HZA is a 90 degree angle so since we know that HZJ is 38 degrees then we will subtract 38 from 90 which will be 52 degrees.

There are 4,431,621,036,503,680 different ways to seat the 60 students in 62 seats.

If there are 60 students and 62 seats, then there will be 2 empty seats in the classroom. We need to find out the number of ways to seat the 60 students in these 62 seats.

To solve this problem, we can use the permutation formula:

nPr = n! / (n - r)!

where n is the total number of objects and r is the number of objects we want to arrange.

In this case, we want to arrange 60 students in 62 seats, so we can use the formula as follows:

62P60 = 62! / (62 - 60)!

= 62! / 2!

= 62 x 61 x 60 x ... x 3 x 2 x 1

= 4,431,621,036,503,680

Therefore, there are 4,431,621,036,503,680 different ways to seat the 60 students in 62 seats.

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The set of the numbers are all integers from 9 to 21 inclusive

It is the collection of items to form a group

All  the members of:

P={odd numbers}

P={9,11,13,15,17,19,21}

Q={Even numbers}

Q= {10,12,14,16,18,20}

U={ positive integer between 9 and 21}

This means that U = {9,10,11,12,13,14,15,16,17,18,19,20,21}

Therefore,  P1 and Q1​

P prime include all the elements in the universal set that are not in the subset P  = {10,12,14,16,18,20}

and Q prime include all the elements in the universal set that are not in subset Q =  P={9,11,13,15,17,19,21}

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Answer:

Reflect ABC over the y axis.  Translate ABC 1 unit to the right.  C is the center, dilate ABC with a scale factor of 2.

Step-by-step explanation: