Alexandra filled out the following information on the back of her monthly statement: a. Find Alexandra’s revised statement balance. b. Does her account reconcile? Checking Account Summary Ending Balance from Statement $1,139.78 Deposits Outstanding $280.67 Total of Checks Outstanding $656.91 Revised Statement Balance Check Register (Balance from checkbook) $763.54
Please explain

Therefore, the factored form of the expression is:(2x - 1)(8x + 5)

Factor pairs of80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

In question 8 This requirement is met by the pair -8 and 24.

In question9 16x² - 8x + 24x - 5

7. We can list all the pairs of numbers that multiply to -80 in order to identify all the factor pairs for this number. These are a few of the pairs:

80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

The biggest integer that divides each of two or more numbers without producing a remainder is known as the greatest common factor (GCF).

For instance, 6 is the highest number that divides both 12 and 18 without producing a residual, making it the GCF of 12 and 18.

The highest common factor (HCF) and greatest common divisor (GCD) are other names for the GCF (HCF).

8. We can seek for two values in the list from question 7 that add up to 16 in order to get the factor pair for -80 that adds to the sum of 16. This requirement is met by the pair -8 and 24.

9. Applying the answer to question 8, we can write 16x2 + 16x - 5 in its expanded form as:

16x² - 8x + 24x - 5

The terms can then be categorised as follows:

(16x² - 8x) + (24x - 5) (24x - 5)

When we take the biggest thing in common between each group, we get:8x(2x - 1) + 5(4x - 1) (4x - 1)

10. As a result, grouping can factor the enlarged form of 16x2 + 16x - 5 as follows:

8x(2x - 1) + 5(4x - 1) (4x - 1)

10. Using the enlarged form from answer 9, we may factor the formula 16x2 + 16x - 5 by grouping:

8x(2x - 1) + 5(4x - 1) (4x - 1)

We can factor it out because we can see that the common factor for both terms is (2x - 1):

(2x - 1)(8x + 5)

As a result, the expression's factored form is as follows:

(2x - 1)(8x + 5)

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Answer:

Step-by-step explanation:

Given the graph of y to be 3x² - 8x + 7, to get the value of x for which the graph function achieves its minimum y value, we need to find its turning point first.

At the turning point, dy/dx = 0

Given y = 3x² - 8x + 7

\(\frac{dy}{dx} = 6x-8\\ at\ turning\ point\ 6x-8 = 0\)

\(6x = 8\\x = \frac{8}{6}\\ x =\frac{4}{3}\)

The y value achieves its minimum at x = 4/3

The probability of not landing on a yellow section when spinning the spinner once is 75%.

Option A is correct

The spinner has eight sections, two of which are yellow. Therefore, the probability of landing on a yellow section is:

P(yellow) = 2/8 = 1/4 = 0.25

To determine the probability of not landing on a yellow section, we can use the complement rule:

P(not yellow) = 1 - P(yellow)

P(not yellow) = 1 - 0.25

P(not yellow) = 0.75 or 75%

Therefore, the probability of not landing on a yellow section when spinning the spinner once is 75%.

Option A is correct

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In geometry, there are several ways to prove that two triangles are congruent, which means that they have the same size and shape. Here are three common methods for proving triangle congruence SSS congruence, ASA congruence, and SAS congruence.

Side-Side-Side Congruence: If all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent. This can be written as:

If AB = DE, AC = DF, and BC = EF, then ∆ABC ≅ ∆DEF

Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent. This can be written as:

If ∠A = ∠E, ∠B = ∠F, and AC = EF, then ∆ABC ≅ ∆DEF

Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent. This can be written as:

If AB = DE, ∠A = ∠E, and BC = EF, then ∆ABC ≅ ∆DEF

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The ramp will upward push to a top of about 18.8 inches at its maximum end.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given, The ramp has a length of 34 inches, The angle of elevation from the ground is 20 degrees.

We can use trigonometry to solve this problem.

The height of the ramp can be found using the following formula:

Height = Length x sin(θ)

where,

"Length" is the length of the ramp

"θ" is the angle of elevation in radians.

To convert the angle of elevation from degrees to radians,

angle in radians = (angle in degrees) x (pi/180)

Substituting the values we have, we get:

angle in radians = 20 x (pi/180) = 0.349 radians

Then, we can calculate the height of the ramp using the formula:

Height = 34 x sin(0.349)

= 18.8 inches (rounded to the nearest tenth)

Therefore, the ramp will rise to a height of approximately 18.8 inches at its highest end.

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Calculating the number of days required using each fraction, we can determine the time it would take for Maggie to reach her goal.

To determine the possible fractions of a mile Maggie can run each day to reach her goal of 100 miles, we need to find unit fractions that evenly divide 100. A unit fraction is a fraction where the numerator is 1.

Let's examine some possible unit fractions and calculate the number of days it would take for Maggie to reach her goal using each fraction:

1/2 mile per day:

In this case, Maggie would run 1/2 mile each day. The number of days it would take to reach 100 miles is 100 / (1/2) = 200 days.

1/4 mile per day:

With this fraction, Maggie would run 1/4 mile each day. The number of days needed to reach 100 miles is 100 / (1/4) = 400 days.

1/5 mile per day:

Running 1/5 mile per day, Maggie would need 100 / (1/5) = 500 days to reach 100 miles.

1/10 mile per day:

Running 1/10 mile per day, Maggie would require 100 / (1/10) = 1000 days to complete 100 miles.

These are just a few examples, and there are many other unit fractions that could be used. In general, Maggie can run any unit fraction that evenly divides 100 to reach her goal.

To find these fractions, we can divide 1 by whole numbers that divide 100 evenly. For example, 1/2, 1/4, 1/5, and 1/10 are examples of unit fractions that evenly divide 100.

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Answer:

$100,000

Step-by-step explanation:

Let the total income of the store = \(\$x\)

Total spends on salaries = \(\frac{1}{4}\) of total income

Total spends on advertising = \(\frac{1}{6}\) of total income

Also, we are given that:

Total money paid as salaries = $150,000

To find:

Total spends on advertising ?

Solution:

As per question statement, we can write the following equation:

\(\dfrac{1}{4}x =\$150000\\\Rightarrow x =\$150000\times 4\\\Rightarrow x = \$600000\)

Now, as per the given statement, total spends on advertising are:

\(\dfrac{1}{6}x =\dfrac{1}{6}\times 600000 = \bold{\$100,000 }\)

Therefore, the answer is $100,000

In doing a quantity takeoff for 100 square feet of single wythe concrete masonry wall, with a thickness of 8", we would need  14.06 8x8x16 block and 10.14 cubic feet mortar.

Number of blocks:

Since each block is 8x8x16 inches, the volume of one block is:

Volume of one block = Length x Width x Height

                                   = 8 inches x 8 inches x 16 inches

                                   = 1024 cubic inches

To calculate the number of blocks needed, we divide the wall area by the area of one block:

Number of blocks = Wall area in square inches / Area of one block

                              = 14,400 square inches / 1024 cubic inches

                              ≈ 14.06

Rounding to the nearest whole number, the correct answer is 14 blocks.

Amount of mortar:

To determine the amount of mortar needed, we multiply the wall area by the joint thickness:

Volume of mortar = Wall area x Joint thickness

                              = 100 square feet x 1 square foot/144 square inches x 8 inches x 3/8 inches

                              ≈ 10.14 cubic feet

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To be ready for an emergency, one must be aware of emergency procedures, know how to reach average emergency services, know where to find safety equipment, and be aware of all exits.

1. Recognize safety precautions and emergency protocols.

2. Make sure emergency personnel's contact information is accessible.

3. Recognize where emergency supplies like first aid kits and lab phones are located.

4. Be sure you are familiar with all building exits in case an evacuation is necessary.

5. Ensure that you have an emergency action plan.

It's critical to have a fundamental awareness of safety measures and emergency protocols in order to be ready for a crisis. Also, it's crucial to keep emergency personnel's contact information close at hand in case you need to get in touch with them. Knowing where to find safety supplies like first aid kits and lab phones might be useful for emergency planning. In case of an evacuation, make sure you are familiar with all building exits. Being more organised can help you be better prepared. Make an emergency plan. You may be better prepared for any situation by keeping an emergency kit containing items like food, water, flashlights, and a first aid kit. Last but not least, it's critical to be informed about any potential emergencies in your neighbourhood and to heed the advice of the authorities if they advise evacuation or other safety measures. By taking these actions, you can make sure that you are as ready as you can be for any situation.

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Answer:

D

Step-by-step explanation:

The upper bound is 1842 and lower bound is 1692. By using these boundaries and t-table, the sample mean is 1767 and sample standard deviation = 133.98.

Here, the two boundaries are 1692 and 1842.

Mean = (1692+1842) /2 = 1767

Here the degree of freedom, df = (n-1) = 25-1 =24

Margin of error = (1842-1692)/2 = 75

Confidence level = 99%

From the t table, value of T with confidence level 99% and df= 24 is 2.80

The equation for margin of error is M = Ts/√n

            M= 75 , T= 2.80, n =25

75 = (2.80 × s) / √25

75 = 2.80s/ 5

s = (75×5)/2.80 = 133.928 = 133.93

So the sample mean is 1767 and the standard deviation is 133.93.

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Answer:

D. trapezoids

Therefore, based on the existence of a Cauchy subsequence, we have proved that the original sequence sn converges.

To prove that the original sequence sn converges based on the existence of a Cauchy subsequence sσ(n), we need to show that the sequence sn is also a Cauchy sequence. A Cauchy sequence is defined as a sequence in which for any positive ε, there exists an index N such that for all m, n > N, |sm - sn| < ε.

Since we have a Cauchy subsequence sσ(n), by definition, for any positive ε1, there exists an index M such that for all i, j > M, |sσ(i) - sσ(j)| < ε1. Now, since the subsequence sσ(n) is a subsequence of the original sequence sn, for any positive ε2, we can choose the same index M and find an index N such that for all m, n > N, |sm - sn| < ε2.

By choosing ε = min(ε1, ε2), we can conclude that for any positive ε, there exists an index N such that for all m, n > N, |sm - sn| < ε. This shows that the original sequence sn satisfies the Cauchy criterion, and therefore, it is a Cauchy sequence. Since every Cauchy sequence in a metric space converges, we can conclude that the original sequence sn converges.

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The general form of the equation of the circle will be x² + y² − 8x − 4y + 11 = 0.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

The standard form of the equation of a circle is (x − 4)² + (y−2)² = 9

Then the general form of the equation of the circle will be

x² + 4² − 8x + y² + 2² − 4y = 9

      x² + y² − 8x − 4y + 20 = 9

        x² + y² − 8x − 4y + 11 = 0

Then the correct option is A.

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Answer:

x=-9

Step-by-step explanation:

The normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

Therefore, the normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

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Answer:

1.0 mL each day

Step-by-step explanation:

The required daily dosage of vitamin D is 10 micrograms.

The supplement contains 5 micrograms per 0.5mL.

The volume of supplement necessary to fulfill the daily requirements of vitamin D is:

\(V=\frac{0.5\ mL}{5\ mcg}*10\ mcg\\ V=1.0\ mL\)

She should administer 1.0 mL of the supplement each day.

Answer:

The angle is 90, my friend gave the answer as 10, so he is incorrect

The complement of the angle is not 10 but 0

The measure of the supplement is 90 degrees

Step-by-step explanation:

The complement of an angle is simply the value of 90 minus the angle

The supplement of an angle is simply the value of 180 minus the angle

So let’s say the angle we are looking at is x

The complement of the angle will be 90 - x

The supplement of the angle will be 180-x

so from the question;

x = 90-x + 180-x

x = 270 - 2x

2x + x = 270

3x = 270

x = 270/3

x = 90

The measure of the angle is 90 degrees

the measure of the complement of this angle is 90-90 = 0 degrees

The measure of the complement is 180-90 = 90 degrees

Step-by-step explanation:

b=3

b-2

=3-2

=1

Hope it helped ❤️

Answer:

620

Explanation:

When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Calculation of the number of elk:

Since the population is 7,750.

The random sample is 50.

So here be like

= 620

hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Answer:

24

Step-by-step explanation:

hope it helps....

it's 100% correct

Answer:

24

Step-by-step explanation:

simplify 48/16

3 = X/8

Multiply both sides by 8

3 × 8 = 24

The constant of proportionality is 0.2

The constant of proportionality for Josiah's speed is 0.2 miles per minute.

To find the constant of proportionality, we can use the formula:

constant of proportionality = distance / time

In this case, we have the distance Josiah skateboards from his house to school is 4 miles, and it takes him 20 minutes.

So, the constant of proportionality is:

4 miles / 20 minutes = 0.2 miles/minute

Therefore, the constant of proportionality for Josiah's speed is 0.2 miles per minute. This means that he skateboards at a constant rate of 0.2 miles per minute from his house to school.

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Answer:

angle dfe = 28°(by vertical opposite angle)

1. Quadratic function with range [-2, ∞): One example is f(x) = x² - 2, which opens upward with a vertex at (0, -2) and includes all values greater than or equal to -2.

1. Quadratic function with range [-2, ∞):

A quadratic function can be written in the form f(x) = ax² + bx + c, where a, b, and c are constants. To find a quadratic function with a range of [-2, ∞), we need to ensure that the function outputs values greater than or equal to -2 for all x.

Let's consider the quadratic function f(x) = x² - 2. This function opens upward since the coefficient of x² is positive. The vertex of the parabola is given by (-b/2a, f(-b/2a)). In our case, b = 0 and a = 1, so the vertex is located at (0, -2).

For any value of x, the function f(x) = x² - 2 outputs a value greater than or equal to -2. As x moves further away from the vertex in either direction, the function value increases without bound, ensuring that the range includes all values greater than or equal to -2.

2. Exponential function with range (-∞, 0):

An exponential function can be written in the form f(x) = a^x, where a is a positive constant. To find an exponential function with a range of (-∞, 0), we need to ensure that the function outputs negative values for all x.

Let's consider the exponential function g(x) = -2^x. By multiplying the standard exponential function f(x) = 2^x by -1, we obtain a reflection across the x-axis. As a result, g(x) is negative for all values of x.

As x approaches positive or negative infinity, the function g(x) approaches 0. Therefore, the range of g(x) is the set of all negative real numbers, represented as (-∞, 0).

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The slant height of the hexagonal pyramid is: B. 14 inches.

Area of a regular hexagon = 3√3/2(s²)

First, find the area of the regular hexagon:

Area = 3√3/2(s²) = 3√3/2(10²) = 150√3 in.².

Surface area is given as 420 + 150√3 in.².

Area of the 6 triangles = surface area - area of hexagonal base = 420 + 150√3 - 150√3

Area of the 6 triangles = 420 in.²

Area of 1 triangle = 420/6 = 70 in.²

Use the area of a triangle to find the slant height (h):

70 = 1/2(10)(h)

2(70) = 10(h)

140/20 = h

h = 14 in.

The answer is B. 14 inches.

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Answer:

e(-6, 10)

f(-10, 10)

g(-3, 1)

Hope this helps.

Answer: 10,985 students

Step-by-step explanation:

You are given the original number of students, the rate of growth and the number of years. The Future value formula can therefore be used:

Number of students in 2010 = Number of students in 1995 * ( 1 + growth rate) ^ number of years

Number of years = 2010 - 1995 = 15 years

Number of students in 2010 = 1,350 * ( 1 + 15%)¹⁵

= 10,985 students