For any positive numbers, a, b and d, with b = 1, logb = d•log b a

The counterexample must satisfy the hypothesis of the conditional statement which is the correct answer would be option (B).

A counterexample is an example in which the hypothesis is correct but the conclusion is incorrect.

Since A counterexample is used to show that a conditional assertion is untrue.

So, just one counterexample is required to prove a statement untrue.

Also, when employing a counterexample to prove a conditional assertion untrue.

The counterexample must then meet the hypothesis of the conditional statement.

As a result, the correct statement concerning the counterexample is;

The conditional statement's hypothesis must be satisfied by the counterexample.

Hence, the correct answer would be option (B).

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Answer:

(3.4,3)

Step-by-step explanation:

(2.7+4.1÷2, -1.2+7.2÷2)

=(6.8÷2, 6÷2)

=(3.4,3)

Solution

- The inequality is:

- The graph of the inequality is graphed using a graphing calculator as follows:

Given the sample mean of the distribution as 9 minutes.

Also, the sample deviation as 2 minutes;

Given the z-score formula;

Where;

Now, from the Z-table;

Thus, the percentage of the calls lasted less than 5 minutes is 2.3%

Answer: im pretty sure its 4 from 3/4

Step-by-step explanation:

Answer:

a= 2 and b= 8

Step-by-step explanation:

a=5/9×18=10

b=4/9×18=8, then a-b=10-8=2

b=4/9×18=8

Given;

There are given that the graph represents the number of siblings.

Explanation:

According to the given graph:

The frequency of the number of siblings is:

Now,

We need to find the value of the range:

So,

From the concept of range:

The value of the difference between the highest data and lowest data will be representing the value of the range:

So,

The highest number is 7 and the lowest data is 2:

So,

Final answer:

Hence, the value of the range is 5.

Answer:

x=27/10

Step-by-step explanation:

move all the terms not containing x to the right side of the equation

Answer:

17/12

1 5/12

Step-by-step explanation:

If we make the fractions have common denominators, this problem is a piece of cake.

First, since the closest multiple of 3 and 4 is 12, put 12 instead of the 3 and 4.

Since 3x4=12, multiply 2x4.

2x4=8.

So the first fraction would be 8/12

Next, since the 4 turned into a 12, multiply 3 by 3.

3x3=9

So the second fraction would be 9/12.

Now, add 9/12 and 8/12 together.

9/12+8/12=

17/12

1 5/12

Answer:

-54g or -9g(5+1)

Step-by-step explanation:

-45g - 9g

-9g(5+1)

I'm not sure which form you want it in lol. -9g(6)

:]

Answer:

-9g ( 5 + 1 )

Step-by-step explanation:

-45g - 9g

-(45g - 9g)

common factor or less number = 9

-9g (5 + 1)

Answer:

D: 9.75 * 10^6

Step-by-step explanation:

You can make it easy for yourself if you write both answers in the same form:

(9.4 * 10^6) = (9.4 *10 *  10^5 = 94*10^5) and (3.5 * 10^5) stays the same.

We can now add those numbers up easier:

(94*10^5) + (3.5*10^5) = ( 94 + 3.5 ) * 10^5 = ( 97.5 * 10^5 )

but this answer is not in the option list. We have to perform the same trick as in the beginning, but than the other way around:

(97.5 * 10^5) = (9.75 * 10) * 10^5 = 9.75 * 10^6,

which is exactly option D

So we are told that the height of the innertube in meters is given by:

The minimum height is 2 meters, the maximum is 8 meters and the time between two consecutive maximums is 12 seconds. Here is important to note a few properties of the sine. First of all, the minimum value of sin(bx) is -1 and its maximum value is 1. Then the height of the innertube is minimum when sin(bx)=-1 and maximum when sin(bx)=1. With these two values we can build two equations for a:

So we have:

Substracting 5 from both sides of the second equation we get:

Using this in the first equation gives us:

Which confirms that a=3. Now we have to find b. For this purpose we can recal another property of the sine. Its period i.e. the distance (in this case the time) between two consecutive maximums is given by:

Since we know this time is 12 seconds we get:

If we multiply both sides by b and divide them by 12 we get:

So we have:

Which means that the answer is the second option.

Given:

The equations are:

a.) y = 2x + 7, b.) y = 3/5x + 1, c.) 3x + 2y = 6, d.) y = x^2

To determine what in the equation of part (d) makes its different, we first note that the graph for part (d) is a parabola, which is a curve with an upward opening. In addition, we also note that the power of x in the equation of part (d) is 2, while the other three graphs have a power of 1.

Therefore, the answer is:

The power of x in the equation of part (d) makes its graph different.

Answer:

14, 200 squared, 15

Step-by-step explanation:

Answer:

The ratio using the word "to" is;

Explanation:

Given on the table;

Number of O+ donors = 100

Number of B+ donors = 29

The ratio of the O+ donors to B+ Donors is:

Number of O+ to Number of B+

Which gives;

The ratio using the word "to" is;

Answer:

  3 ≤ x < ∞

Step-by-step explanation:

You want the domain of a square root function shifted right 3 units and up 1 unit. It goes through points (3, 1), (4, 2) and (7, 3).

The domain of a function is the set of values of the independent variable for which the function is defined. It is the horizontal extent of the graph.

The graph of the given square root function extends to the right from x=3.

The domain is 3 ≤ x < ∞. In interval notation, it is [3, ∞).

GIVEN:

We are told that a school wants to estimate the number of students who drive to school.

Required:

To determine which survey would best represent the entire student population..

Step-by-sep solution;

Taking a sample of 11th graders would not correctly represent the entire student population. The result from this survey would at best represent the preference of 11th grade students and not other grades. The same thing applies to a survey of the science club. The science club cannot accurately represent all students (including other clubs).

However, a survey of 25 students from the school would best represent the entire student population since there is a probability of every category of student being represented.

Therefore,

25 students are randomly selected from the school; 4 drive to school.

Part (B):

There are 1750 students at Lincoln High. Use the answer above to estimate the number of students who drive to school.

If the sample of 25 students has 4 students who drive to school, then to estimate the entire population based on this;

Therefore, we now have;

ANSWER:

Find the intercepts and domain and perform the symmetry test on each of the following hyperbola

9x² - 16y² = 144

Domain (-inf, -4] and [4, inf)

Symetry around y-axis

There is no y intercepts

X-intercepts at x = -4 and x = 4

Focus at (-4, 0) and (4, 0)

5. Given

You know that:

a=-1

b=2

w=-10

Replace these values into the expression:

Following the order of operations, first, you have to solve the exponent and the multiplication:

Both minus signs form a "double negative" when this happens, the signs cancel each other and turn into a plus sign, so that:

Next, solve the addition

The result of this operation is 21.

Answer:

99

Step-by-step explanation:

You can set up a proportion, and solve for the variable (missing grade in this case):

[tex]\frac{88+90+94+89+x}{5} =92[/tex]

Each grade is already in the database, so it can serve as the constant, and five is the denominator because to get a mean average, you must divide all the values by the number of values that exist. So, in this case, it would be 5, 4 including the missing grade, making it 5. Set the equation equal to 92, because that's her desired average, then just solve for x.

Multiply the 5 on both sides.

-> 5 cancels on left, and 5 multiplies with 92 to get 460.

[tex](5)\frac{88+90+94+89+x}{5} = 92(5)[/tex]

Add all constants on the left side of the equation.

-> 88+90+94+89=361

[tex]361+x = 460[/tex]

Subtract that new constant (361) from the 460, and you get x=92.

-> 460-361=99

[tex]x=99[/tex]

Hope this helped. :)

The other point through which a line that describes a proportional relationship must pass is the point (0, 0)

A proportional relationship is one in which each the ratio of the x and y–values of each point on the line of the function is a constant.

The given relationship described by the line = A proportional relationship

The given point on the line = (6, 2)

Required; The other point through which the line must pass.

Given that the relationship described by the line, the ratio of all points on the line is a constant and each point (x, y) can be expressed in the form;

y = K•x

Which gives;

[tex] \displaystyle{ K = \frac{y}{x} }[/tex]

Where, K is a constant which is not equal to zero.

From the zero product property, which states that the product of all numbers and zero is also zero, we have;

When x = 0, k × 0 = 0 = y

A point through the line must pass is therefore; (0, 0)

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Long Multiplication

1. Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand.

This will be written as follows:

467

x 48

---------------

2. Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number.

This product is 8*7 = 56

3. If that answer is greater than nine, write the ones place as the answer and carry the tens digit.

We should write 6 and carry 5:

467

x 48

---------------

6 (carry 5)

4. Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so.

The next product is 8*6 = 48. Adding the carry: 48+5=53, Write 3, carry 5:

467

x 48

---------------

36 (carry 5)

Multiply 8*4 = 32. Add the carry 5: 32+5 = 37. Write the full number because it's the last of the products of this step:

467

x 48

---------------

3736

5. When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.

Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.

Multiply 4*7 = 28. Write 8, carry 2.

467

x 48

---------------

3736

8 (carry 2)

Multiply 4*6=24. Add 2: 24+2=26. Write 6, carry 2:

467

x 48

---------------

3736

68 (carry 2)

Multiply 4*4=16. Add 2: 16+2=18. Write the full number:

467

x 48

---------------

3736

1868

6. When you finish multiplying, draw another answer line below your last row of answer numbers.

467

x 48

---------------

3736

1868

----------------

7. Use long addition to add your number columns from right to left, carrying as you normally do for long addition.

467

x 48

---------------

3736

1868

----------------

22416

Let g represent gallons of water and let L represent loads.

Here, the gallons of water varies directly with the number of loads, thus we have:

g ∝ L

Now introduce a constant k:

g = kL

65 gallons is used to wash 5 loads, thus we have:

65 = k * 5

Let's solve for k:

65 = 5k

Divide both sides by 5:

To find the amount of water that will be used to wash 8 loads, we have:

g = kl

We are to find g, substitute 13 for k and 8 for l:

g = 13 x 8

g = 104

Therefore, to wash 8 loads, 104 gallons of water is needed.

ANSWER:

104

The point-slope form of the equation of a line is given by the following expression:

y - y1 = m(x - x1)

Where m is the slope of the line and (x1, y1) is a point where the line passes through.

The slope of the line can be determined with the following formula:

Where (x1, y1) and (x2, y2) are two points where the line passes through. In this case we are told that the line passes through the points (-2,-6) and (6,5). By replacing the x and y coordinates of these points into the formula of the slope, taking x1 as -2, x2 as 6, y1 as -6 and y2 as 5, we get:

Then, the slope of the line equals 11/8, by replacing 11/8 for m into the slope-point form, we get:

y - y1 = 11/8(x - x1)

By taking one of the points, for example (-2,-6), we replace the x and y-coordinates that appear in the equation of the line, to get:

y - (-6) = 11/8(x - (-2))

y + 6 = 11/8 (x + 2)

Then, the equation of the line in slope-point form is y + 6 = 11/8 (x + 2)

Using operations with mixed numbers and relations between hours and minutes, it is found that:

a) You will arrive in Seattle at 4:15 am.

b) You will arrive in Atlanta at 9:50 a.m.

c) You will arrive in Atlanta at 10:30 a.m.

A mixed number is represented as follows:

a b/c.

In which:

As a decimal, the number is given as follows:

a + (b/c).

For item a, it is found that the time it takes to arrive in Seattle from Atlanta is given by the addition of these following numbers:

Hence the time in hours is:

2.25 + 1.5 + 3.5 + 1.75 + 0.75 = 9.75 hours = 9 hours and 45 minutes.

Seattle is 3 hours behind Atlanta, hence the time you arrive there is:

6:30 pm + 9 hours and 45 minutes = 4:15 am, as:

For item b, we have that:

For item c, 2/3 of an hour is 40 minutes, 40 minutes after 9:50 am is 10:30 a.m., which is the time you would arrive.

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The account balance at the end of the month is $1051.

To estimate the balance in a bank account, one has to add the credit to the available balance of the account and subtract the debited amount from the same.

It is given that the account balance initially is $843.

The deposited balances are $92, $404, $39 and $51.

Add the credited amount to the account balance.

So, the current amount is = $843+ $92+ $404+ $39+ $51= $1429

The withdrawal amount is $70, $87 and $221

Subtract the debited amount to the account balance.

So, the current amount is = $1429 - $70 -$87 - $221 = $1051.

So, the account balance at the end of the month is $1051.

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You have the following expression:

log(z) - log(18)

By the properties of logarithms, consider that the subtraction of two logarithms is equal to the logarithm of the quotient of the arguments:

log(z) - log(18) = log(z/18)

Hence, the answer is log(z/18)