Write an equation to solve for x.

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Answer:

Step-by-step explanation:

Finding the x-intercepts :

Finding the vertex :

Finding the y-intercept :

In order to find x-intercept, the f(x) or y will be 0

=================

(x-4)(x + 2) = 0

(x-4) = 0, (x + 2) = 0

x = 4, x = -2

x intercepts: (4, 0) and (-2, 0)

In order to find vertex use the formula: x = -b/2a

y = (x-4)(x + 2)

y = x² -4x + 2x -8

y = x² - 2x -8

Now find x-coordinate of vertex:

x = -(-2)/2(1)

x = 2/2

x = 1

y coordinates: (1-4)(1 + 2) =  -9

Ordered pair of vertex: (1, -9)

In order to find y intercept, insert x = 0

y = (0-4)(0 + 2)

y = -8

y intercept: (0, -8)

a = y2 / (b^x2) ,To find the initial value of an exponential function, you can use the formula y = a * b^x, where y represents the final value, a represents the initial value, b represents the base, and x represents the exponent.

To solve for the initial value (a), you need to have at least two points on the exponential function. Let's say you have the point (x1, y1) and (x2, y2).

Step 1: Substitute the values of x1, y1, x2, and y2 into the formula y = a * b^x.

Step 2: Since the goal is to find the initial value (a), we can set up two equations using the given points.

For the first point (x1, y1):
y1 = a * b^x1

For the second point (x2, y2):
y2 = a * b^x2

Step 3: Divide the second equation by the first equation to eliminate the base (b):

y2/y1 = (a * b^x2) / (a * b^x1)

Step 4: Simplify the equation:

y2/y1 = b^(x2 - x1)

Step 5: Take the logarithm of both sides of the equation to isolate the exponent (x2 - x1):

log(y2/y1) = (x2 - x1) * log(b)

Step 6: Solve for (x2 - x1):

(x2 - x1) = log(y2/y1) / log(b)

Step 7: Substitute the value of (x2 - x1) into either of the original equations to solve for a:

a = y1 / (b^x1)

or

a = y2 / (b^x2)

Remember to use the same base (b) in all calculations. This will help you find the initial value (a) of the exponential function.
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Answer:

60 minutes

Step-by-step explanation:

Latitude and longitude are measuring lines used for locating places on the surface of the Earth. They are angular measurements, expressed as degrees of a circle. A full circle contains 360°. Each degree can be divided into 60 minutes, and each minute is divided into 60 seconds.

One degree of latitude is equal to approximately 60 nautical miles or 69 statute miles. Since a minute of latitude is one-sixtieth of a degree, it follows that one degree of latitude is equal to 60 minutes.

This means that there are 60 nautical miles or 69 statute miles between two points that differ by one minute of latitude.

The minute of latitude is a widely used unit for measuring distances on Earth, particularly in navigation and aviation. It allows for precise calculations and is crucial for determining positions accurately. Understanding the relationship between degrees of latitude and minutes helps in determining distances, estimating travel times, and ensuring accurate navigation across the globe.

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The fraction of the cake that was ron's pieces is 1/5.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Since Mrs Jones gave 1/5 of a cake to her neighbour, the remaining fraction will be:

= 1 - 1/5

= 4/5

The fraction of the cake that was ron's pieces will be:

= 2/(1+3+4) × 4/5

= 2/8 × 4/5

= 8/40

= 1/5

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Answer:

P = $300

r = 0.15

n = 12

$544.61  (to the nearest cent)

\(P(1+r)^t\)

$524.70  (to the nearest cent)

Step-by-step explanation:

P = principal amount = $300

r = annual interest rate in decimal form = 15% = 15/100 = 0.15

n = number of times interest is compounded per unit t = 12

How much she'll owe in 4 years

P = 300

r = 0.15

n = 12

t = 4

\(P(1+\frac{r}{n})^{nt}=300(1+\frac{0.15}{12})^{12 \times 4}\)

= $544.61  (to the nearest cent)

Yearly compounding interest rate

\(P(1+r)^t\)

How much she'll owe in 4 years at yearly compounding interest

\(P(1+r)^t=300(1+0.15)^4\)

= $524.70  (to the nearest cent)

Answer:

21 chocolate flavored and 42 other flavors

Step-by-step explanation:

\(63 \times \frac{1}{3} = 21 \\ 63 - 21 = 42\)

The distance from his home to his work place is 118.125 miles

He drove from home to work at an average speed of 45 mph. Therefore,

speed = 45 mph

let

time = x

speed = distance / time

distance = 45x

His return trip home took 45 minutes longer because he could only drive at 35 mph. Therefore,

45 minutes = 0.75 hours

distance = 35(x + 0.75)

distance = 35x + 26.25

Therefore,

45x = 35x + 26.25

45x - 35x = 26.25

10x = 26.25

x = 26.25 / 10

x = 2.625

Therefore,

distance = 45(2.625) = 118.125 miles

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Answer:

hsjsh

Step-by-step explanation:

bzbdbdbcjcifhfh

The real number √21 is an example of an irrational number. (Correct choice: C)

According to number theory, real numbers are formed by the following sets:

Then, by direct inspection we get the following conclusions:

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An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.

An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.

In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.

The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.

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Answer: 64 m^3

Step-by-step explanation:

V=1/3*a^2*h

V = 1/3*64*3

V=64 m^3

Answer:

64 m³

Step-by-step explanation:

Formula

\(\textsf{Volume of a square based pyramid}=\dfrac{1}{3}a^2h\)

where:

Given:

Substituting the given values into the formula:

\(\begin{aligned}\implies \textsf{Volume}& =\dfrac{1}{3} \cdot 8^2 \cdot 3\\\\& = \dfrac{3}{3} \cdot 64\\\\& = 1 \cdot 64\\\\& = 64\:\sf m^3\end{aligned}\)

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer:

substitute all given values in this formula v=base ×height

then height= base /volume

Step-by-step explanation:

The correct option is: d. No. There are no free variables since the matrix must have 5 pivots

If the equation Ax=b is consistent for every b in R, it means that the matrix A is invertible, since the solutions to the equation can be expressed as x = \(A^(^-^1^)\)b.

An invertible matrix has full rank, which means that it has 5 pivots in this case.

If Ax=b has more than one solution for some b, then there would be two different vectors x₁ and x₂ that satisfy the equation, which implies that A(x₁ - x₂) = 0.

This means that the matrix A has a nontrivial nullspace, which contradicts the fact that A has full rank. Therefore, it is not possible for Ax=b to have more than one solution for any b in R.

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Jozef's hourly rate, we need to divide his weekly pay by the number of hours he works in a week. Therefore, Jozef's hourly rate is £8.80.

Simply said, an hourly rate is the amount of money you get paid for each hour of labour. If you want to be successful in business, you must grasp how to calculate your time using this hourly salary rate.  

By dividing the weekly hours worked by the number of weeks in a year, 52, you can first calculate the overall number of hours worked. Divide this amount by the yearly salary next.

Jozef's weekly pay = £352

Jozef's number of working hours per week = 40

Jozef's hourly rate = weekly pay / number of hours per week

Jozef's hourly rate = £352 / 40

Jozef's hourly rate = £8.80

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Answer:

Step-by-step explanation:

To get the cost per desk, divide the total cost by the number of desks.

R840 000 x 3,450 desks = R242.86 per desk for Provider 1.

R760 000 R2250 desks = R338.89 per desk

According to the aforementioned computation, Provider 1 is less expensive than Provider 2 since the cost per desk is R242.86 vs R338.89 for Provider 2.

As a result, Provider 1 is less expensive than Provider 2.

The required expected value of the score is 4.92.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

A long hit with success has a 0.4 chance of happening. The following formula can be used to determine which strategy—the short hit or the long hit—will improve the expected value of the score:

Expected value of long hit = P(successful hit)4.2 + P(unsuccessful hit)5.4

= 0.4×4.2 + (1 - .04)×5.4

= 4.92

Thus, required score is 4.92.

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The total area of the figure = area of rectangle + area of triangle = 241 sq. m.

Thus:

Total area of the figure = area of rectangle + area of triangle

= length × width + 1/2 × base × height

Total area of the figure = 12 × 9 + 1/2 × 19 × 14

Total area of the figure = 241 sq. m.

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Answer:

241 square meters

Step-by-step explanation:

edmentum/plato

Answer:

b)

Step-by-step explanation:

9 × (588/2)

= 9 × (294)

= 2646

Answer:

$12.25

Step-by-step explanation:

Part = (percent) whole

x = (3.5) 5

x = $17.5   <------- regular price

x = (.7) 17.5

x = $12.25     <--------- marked down price

Percentage is a way to describe a part of a whole. The sale price of the calculator whose original price was $5 is $12.25.

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

We know that the original price of the calculator is $5, and when the price of the calculator is marked it is 350% of the original value. therefore, the marked up price of the calculator can be given as,

\(350\% of\ \$ 5 \\\\= \dfrac{350}{100}\times 5\\\\= \$17.5\)

Thus, the marked-up price of the calculator is $17.5.

Now, as the store gives a 30% discount on the marked-up value of the calculator, therefore, the price of the calculator will be 70% of the marked up price of the calculator,

\(70\% of\ \$ 17.5 \\\\= \dfrac{70}{100}\times 17.5\\\\= \$12.25\)

Hence, the sale price of the calculator whose original price was $5 is $12.25.

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Angular speed of the fan in radians per minute is 421 (crad /min) , The linear speed of the tip of a blade in inches per minute is

Suppose the dan turns at a rate of 69 revolutions per minute.

Angular speed of the fan in radians per minute is

According to the problem

w = 2zn

(a)  w = 2z * 67  

= 134z

≈ 421 crad /min)

Angular speed of the fan in radians per minute is 421 (crad /min)

The linear speed of the tip of a blade in inches per minute is

(b) v = 2z * 19 * 67

{ v = 2zrn}

=2546z

7988(cin / m * in)

The linear speed of the tip of a blade in inches per minute is 7988(cin / m * in)

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SOLUTION:

Case: Averages

Method:

Sample 1

Mean

Sample 2

Mean

Sample 3

Mean

b) Range of sample means:

R = 4.75 - 4.25

R = 0.5

c)

The following statements are valid:

i) The closer the range of the sample mean is to 0. The more confident they can be in their estimate

iii) The mean of the sample mean will tend to be a much better estimate than a single sample mean.

Final answers:

a)

SAMPLE 1. m = 4.25

SAMPLE 2. m = 4.75

SAMPLE 3. m = 4.75

b) Range = 0.5

c)

i) The closer the range of the sample mean is to 0. The more confident they can be in their estimate

iii) The mean of the sample mean will tend to be a much better estimate than a single sample mean.

Answer:

$648.00

Step-by-step explanation:

==>Given:

Squared living room of 9m by 9m

Cost of purple carpet per m² = $8.00

==>Required:

Cost of buying carpet to cover the squared living room

==>Solution:

Find the area of the room:

Area of squared room = 9m × 9m = 81m²

Find cost of purple carpet that would cover 81m²:

Let x be the cost of carpet required to cover the room.

Thus,

1m² = $8.00

81m² = x

cross multiply

1*x = 8.00*81

x = 648

Cost of purple carpet to cover the living room = x = $648.00

Step-by-step explanation:

Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.