14 − 3x < −1
What is x?

You have a box that contains g amount of cookies and you are given an additional 3 cookies. How many cookies are in the box (g) if you wanted to put all the cookies into 6 bags, with them all containing 15 each?

Answer:

x = 19; y = 19√3

Step-by-step explanation:

sin 30° = opp/hyp

sin 30° = x/38

x = 38 × sin 30°

x = 19

cos 30° = adj/hyp

cos 30° = y/38

y = 38 × cos 30°

y = 38 × √3/2

y = 19√3

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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Amplitude of  f(x)=5cosx

= 5

The amplitude of a periodic variable is a measure of its change in a single period. The amplitude of a non-periodic signal is its magnitude as compared with a reference value. there are numerous definitions of amplitude, which can be all functions of the magnitude of the differences between the variable's extreme values.

It refers to most displacement from the equilibrium that an object in periodic motion show. as an example, a pendulum swings through its equilibrium point (straight down), and then swings to a maximum distance away from the center.

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Using a trigonometric relation we can see that the value of the missing side is x = 3.9

We can use the trigonometric relation:

cos(75°) = adjacent cathetus/hypotenuse

Where the adjacent cathetus is x, and the hypotenuse measures 15 units, then we can replace these values to get.

cos(75°) =x/15

Solving this for x we get.

15*cos(75°) =x

3.9 = x

So the correct option is D, the length of the missing side is 3.9 units.

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a. The teacher can expect the batteries to last at least 92.09 days  on minimum average.

b. The teacher will need to spend at most $49.92 on batteries for calculators over the year.

What is minimum average day?

a. The margin of error of ‡9% means that we can be 95% confident that the true average number of days the batteries will last is within 9% of the sample average. To find the minimum average number of days a teacher can expect to have the batteries last in her classroom, we subtract the margin of error from the sample average:

Minimum average = 101 - (0.09)(101) = 92.09 days (rounded to two decimal places)

Therefore, the teacher can expect the batteries to last at least 92.09 days on average.

What is spend ?

b. The total number of batteries required for the 24 TI-84 calculators is:

24 calculators x 4 batteries per calculator = 96 batteries

The total cost of the batteries will be:

96 batteries x $0.52 per battery = $49.92 (rounded to two decimal places)

Therefore, the teacher will need to spend at most $49.92 on batteries for calculators over the year, assuming all batteries need to be replaced.

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If this week there are 144 members at the meeting, which is 90% of the total group, the total number of members on the green team is 160.

If 144 members represent 90% of the total group, we can set up the equation:

144 = 0.9x

where x is the total number of members on the green team.

To solve for x, we can divide both sides of the equation by 0.9:

144 ÷ 0.9 = x

This simplifies to:

160 = x

To check our answer, we can verify that 144 is indeed 90% of 160:

144 ÷ 160 = 0.9

which confirms that our answer is correct.

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Answer:

X=42

Step-by-step explanation: x-23=17 you would do the inverse of subtracting which would be addition which would be 23+17 which equals  42

Answer:

\(Cost = \$28\)

Step-by-step explanation:

Given

Represent Goldfish with g and hermit crabs with h.

The first statement, we have:

\(7g + 3h = 26\)

The second statement, we have:

\(4g + 5h = 28\)

Required

Determine the selling price of 6 goldfish and 4 hermit crabs

The equations are:

\(7g + 3h = 26\) --- (1)

\(4g + 5h = 28\) --- (2)

Make g the subject in (2)

\(4g + 5h = 28\)

\(4g = 28 - 5h\)

Divide both sides by 4

\(g = \frac{1}{4}(28 - 5h)\)

Substitute \(\frac{1}{4}(28 - 5h)\) for g in (1)

\(7g + 3h = 26\)

\(7(\frac{1}{4}(28 - 5h)) + 3h = 26\)

\(\frac{7}{4}(28 - 5h) + 3h = 26\)

Multiply through by 4

\(4 * \frac{7}{4}(28 - 5h) + 4*3h = 26*4\)

\(7(28 - 5h) + 4*3h = 26*4\)

Open bracket

\(196 - 35h + 12h = 104\)

\(196 -23h = 104\)

Collect Like Terms

\(-23h = 104-196\)

\(-23h = -92\)

Make h the subject

\(h = \frac{-92}{-23}\)

\(h = \frac{92}{23}\)

\(h = 4\)

Substitute 4 for h in \(g = \frac{1}{4}(28 - 5h)\)

\(g = \frac{1}{4}(28 - 5*4)\)

\(g = \frac{1}{4}(28 - 20)\)

\(g = \frac{1}{4}(8)\)

\(g = 2\)

This implies that:

1 goldfish = $2

1 hermit crab = $4

The cost of 6 goldfish and 4 hermit crabs is:

\(Cost = 6g + 4h\)

\(Cost = 6*\$2 + 4*\$4\)

\(Cost = \$12 + \$16\)

\(Cost = \$28\)

The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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Answer:

38.88

Step-by-step explanation:

Convert the problem to an equation using the percentage formula: P% * X = Y.

P is 10%, X is 150, so the equation is 10% * 150 = Y.

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.

Answer:

28 words Maria got right

Step-by-step explanation:

70% of total words Maria got right

Therefore:

\(\frac{70}{100} *40= 28\)

Answer:

5040 different combinations

Step-by-step explanation:

0-9 = 10 numbers

1st digit can be 1 0f 10

2nd digit can be 1 of 9

3rd digit can be 1 of 8

4th digit can be 1 of 7

10×9×8×7=5040

The graph of the absolute value function:

g(x) = |2 + x| - 3

Can be seen at the end of this answer.

Here we want to graph the absolute value function:

g(x) = |2 + x| - 3

First, we know that the vertex of this function will be at the point (-2, -3) (is at the value of x such that the absolute value part becomes zero).

From that vertex, we just draw two lines with slope 1 to the right and -1 to the left, you should get something like the graph below.

As you can see it opens upwards, because the leading coefficient is 1 (positive).

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Answer:

-1/2

Step-by-step explanation:

We know

The dilation of K(-2,4) equals K'(1,-2)

To get from -2 to 1, we time -1/2

To get from 4 to -2, we time -1/2

So, the scale factor used for the dilation is -1/2

Rewriting the given equation using common factor, we get -

"one fourth times x times y times the quantity x squared plus 3 times y end quantity"

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is the following statement -

"one fourth times x cubed times y plus three fourths times x times y squared".

first we will convert the given statement into the mathematical equation as follows -

(1/4)x³ y + (3/4)xy²

To write it using the common factor, we can proceed as follows -

(1/4)xy[x² + 3y]

The common factor is (1/4)xy

Now, we will convert the equation in the form of a statement as follows -

"one fourth times x times y times the quantity x squared plus 3 times y end quantity"

Therefore, rewriting the given equation using common factor, we get -

"one fourth times x times y times the quantity x squared plus 3 times y end quantity"

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Answer:

41200

Step-by-step explanation:

Answer: Type I error

Step-by-step explanation:

A type 1 error is also referred to as the false positive and it is when a true null hypothesis is incorrectly rejected by the researcher.

On the other hand, type II error which is also refered to as the false-negative is when a null hypothesis which is false is failed to be rejected by the researcher but rather accepted.

Based on the information given in the question, since the data leads to the rejection of the null hypothesis such was later found out to be true, then a type I error has occured.

Answer:

4x=0 x=0

Step-by-step explanation:

Answer:

A option A is the write answer

Answer:

pentagon

regular polygon

Step-by-step explanation:

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer:

because it is a triangle we square the lenght and equate to the other side,and square all the other side

X²=20²+10²

X=√20²+10²

=22.36m

The values of the trigonometry functions are sin(θ) = 3/√13, cos(θ) = 2/√13, tan(θ) = 3/2, csc(θ) = √13/3, sec(θ) = √13/2 and cot(θ) = 2/3

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

The right triangle

The hypotenuse of the right triangle is calculated as

h² = 2² + 3²

When evaluated, we have

h = √13

The values of the trigonometry functions are then evaluated as

sin(θ) = 3/√13

cos(θ) = 2/√13

tan(θ) = 3/2

csc(θ) = √13/3

sec(θ) = √13/2

cot(θ) = 2/3

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The slope of the line represented by the graph of a linear function is  -5/2

The general equation of a straight line is -

y = mx + c

where -

m → slope of line

c → y - intercept of line

here, we have,

Given in a question a linear function that decreases from left to right passing through the coordinates A(0,3) and B(2, -2).

A linear function is a function of general equation → y = ax + b which is same as y = mx + c.

So, it represents a straight line.

The line passes through the points A (0,3) and  B (2, -2).

The Slope of the given line can be calculated using the following formula -

m = (y[2] - y[1]) / (x[2] - x[1])

m = (- 2 - 3) / (2 - 0)

m = -5/2

Therefore, the slope of the line represented by the graph of a linear function is  -5/2.

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Answer:

.49 if you're dividing them.

Step-by-step explanation:

The system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased is:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Wyatt purchased 2 more bottles of juice than bottles of soda, hence:

y = x + 2.

Each bottle of soda has 30 grams of sugar and each bottle of juice has 40 grams of sugar, and a total of 430 grams was purchased, hence:

30x + 40y = 430.

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