The measure of one angle is 10° less than one-fourth the measure of its complement. Find the measures of the two angles 。 and the measure of the larger angles The measure of the smaller angle is

Dahila's Child and Dependent Care Credit in 2022 would be $6,000.

The Kid and Ward Care Credit is a tax cut that can assist with balancing the expenses of really focusing on qualified youngsters and wards. How much the not entirely set in stone by the person's changed gross pay (AGI) and the sum they spend on care? In the event that the AGI is underneath $125,000, the individual can get a credit equivalent to half of their childcare costs.

In 2022, Dahila brought about $12,000 in kid care expenses and has an AGI underneath $125,000, so her Kid and Ward Care Acknowledge would be determined as follows:

$12,000 x 50% = $6,000

Therefore, Dahila's Child and Dependent Care Credit in 2022 would be $6,000.

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The limits of the function as x approaches infinity and negative infinity are 0 and negative infinity, respectively, and the horizontal asymptote is y = 0.

A function is a mathematical rule that assigns a unique output for each input.

For the function

=> f(x) = 3x²+2/x³√4x⁶+1,

we will evaluate the limits as x approaches infinity and negative infinity. We will also determine the horizontal asymptote of the function.

When x approaches infinity, the denominator

=> x³√4x⁶+1

becomes very large, so the value of the function becomes very small. Thus, the limit of the function as x approaches infinity is 0.

To determine the horizontal asymptote, we need to look at the degree of the numerator and denominator.

The numerator has a degree of 2 and the denominator has a degree of 3. Since the denominator has a higher degree, the horizontal asymptote is y = 0.

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Answer:

ang. PQR

Step-by-step explanation:

The diameter which subtends an angle to the circumference of the circle is equal to 90 degrees. Hence, either ang. PQR and ang. PSR are both right angles.

Answer: The normal probability plot is a graphical technique for assessing whether or not a data set is approximately normally distributed. The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line.

Step-by-step explanation:

The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot.

The normal probability plot is a graphical method for determining whether or not a data set is roughly normally distributed . The points in the data are displayed against a hypothetical normal distribution such that they should roughly form a straight line.

The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot. It is applied to ascertain if a tiny amount of data is representative of a normal distribution.

A graphical method for locating significant deviations from normalcy is the normal probability plot. Outliers, skewness, kurtosis, the requirement for transformations, and mixes are some examples of this. The raw data, residuals from model fits, and estimated parameter values are used to create normal probability charts.

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Answer:

Step-by-step explanation:

Because the numbers -2 3/4 and 5/9 are rational, and the sum of 2 rational numbers are always rational.

Answer:

Always true

Step-by-step explanation:

A rhombus is a parallelogram with equal sides, and a square is a rectangle with equal sides. As a rectangle can also be a parallelogram, you can prove that a square is always a rhombus.

Answer:

This is always true.

Step-by-step explanation:

They both have 4 congruent sides

Answer:

d

Step-by-step explanation:

D. 24 humans and 50 horses.

We can use a system of equations to solve for the number of horses (x) and number of humans (y):

x + y = 74 (the total number of heads)

y = 196 - 4x (the total number of legs, with each horse having 4 legs)

Substituting the second equation into the first:

x + (196 - 4x) = 74

5x = 122

x = 24.5 (number of horses rounded down to the nearest whole number)

y = 74 - x = 50 (number of humans)

Answer:

Answer should be

Step-by-step explanation:

The process takes approximately 14 iterations to reach the desired accuracy.

The Bisection Method will take approximately 14 iterations to find the approximate root of the equation within an error tolerance of 0.001. The mathematics calculations involve finding the midpoint of a given interval [a, b] and then determining whether the midpoint is a root of the equation. If it is not a root, then the interval is divided into two halves, and the process is repeated on the subinterval where the sign of the function changes. This process is repeated until the midpoint is within the desired error tolerance.

To calculate the number of iterations required, we begin by noting that the initial interval used is [1, 0]. The midpoint of this interval is 0.5. This value is then plugged into the function to determine if it is a root. Since it is not, the interval is then divided into two halves and the process is repeated. This process is repeated until the midpoint is within the desired error tolerance of 0.001. In this case, it takes approximately 14 iterations to reach the desired accuracy.

The complete question is:

Given the function f(x) = x^3 - x^2 - 4 and an initial approximation of x = 1, how many iterations of the Bisection Method are required to find the approximate root of the equation within an error tolerance of 0.001?

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Answer: The volume of a sphere can be calculated using the formula:

V = (4/3)πr^3

Where V is the volume and r is the radius of the sphere.

Given that the volume is 36 cubic inches, we can substitute into the formula:

36 = (4/3)πr^3

Dividing both sides by (4/3)π:

36 / (4/3)π = r^3

Taking the cube root of both sides:

r = ∛(36 / (4/3)π)

The radius of the sphere is approximately 2.74 inches.

Step-by-step explanation:

The speed of the airplane in still air is 21.5 mph.

An airplane flying with the wind takes 2 hours with a 25-mph tailwind to reach its destination. the return trip takes 4 hours flying against the wind.

We must calculate the wind speed from the ground speed and airspeed as we cannot measure the wind speed directly from the aeroplane.

Flying at 35 mph requires four hours. Consequently, the distance is

25 * 2 = 50 miles.

For the same route, a return trip takes 5 hours.

Hence V-Vs= 50/4 = 12.5.

Therefore, V+Vs= 25 (1).

V-Vs = 12.5-----(2).

We obtain V=21.5 mph Vs=2.5 mph by solving for (1) and (2).

Thus, V = 21.5 mph is the airplane's windless speed.

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The potential causes for extreme emotion are Chemical imbalance, drug use, mild stress

When someone starts displaying extreme emotions, we frequently discover that they lack emotional control, are brave, and occasionally even are annoying. This person reacts in an exaggerated way to any situation or circumstance, no matter how unimportant it may seem.

However, biological factors and other factors that interfere with a person's psyche can cause these emotions to be triggered, leading to the externalization of exaggerated emotions. Chemical imbalance, drug use, and mild stress are a few of these factors.

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The exponential function calculator available online at BYJU speeds up the calculation and displays the value of the variable quickly.

The e key must be pressed first on the majority of graphing calculators, followed by the exponent key and the exponent input keys, in order to raise e to a power.

Using the free online tool known as the exponential function calculator, you can see the exponent's fluctuating value. The calculation is accelerated by the use of BYJU's online exponential function calculator, which also shows the variable's value in a little amount of time.

Directly below the display area, there is a row of sophisticated operators and features. The Down arrow to the right can be used to access more complex operators and functions. pi (π), superscript for exponents (^), cosine (cos), tangent (tan), logarithm (ln, log), and square root (√) are some of the buttons you'll encounter.

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Cellphone carriers charge a monthly fee and a per-minute rate. Every minute costs $0.06, so Option C is correct. Part 2, the carrier charges $60 monthly.

To obtain the constant rate of 0.06, we can use the two equations from January and February to solve for x, the constant rate:

Let x be the constant rate and y be the fixed monthly fee.

We can use these two equations to find the constant rate. Solving for x in the first equation, we get:

Next, we substitute this expression for x into the second equation:

Finally, we solve for x:

So, the constant rate is 0.06 dollars per minute.

To find the fixed monthly fee, we can use the constant rate of 0.06 and one of the equations from January or February.

For January: y + 150x = $69

Substituting the constant rate x = 0.06, we have:

So, the fixed monthly fee is $60.

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Both Isaac and Micah are using a compass and straightedge for their constructions.

The differences between their construction steps are:

Isaac is constructing congruent segments, which means he is dividing the original line segment into equal parts, while Micah is constructing a segment bisector, which means he is dividing the line segment into two equal parts and finding the midpoint.

Isaac only needs to mark one point on the line segment with his compass to get two congruent segments, while Micah needs to mark two points and then find the midpoint between them.

The final results of their constructions are different: Isaac will have two congruent line segments, while Micah will have one line segment bisector that splits the original line segment in half.

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The total distance the tourist has to pay the taxi driver is the sum of the distance the tourist walked and the distance the taxi drove, or 8 miles + 100 miles = 108 miles.

The distance the tourist has to pay the taxi driver can be calculated using the formula for distance = rate x time.

First, let's find out how far the tourist walked. We know that he walked at a rate of 4 mph for 2 hours, so the distance he walked is 4 mph x 2 hours = 8 miles.

Next, let's find out how far the taxi drove. The taxi reached the destination 2 hours after the tourist started walking, so the time it took for the taxi to reach the destination is 2 hours. The taxi was traveling at a constant speed of 50 mph, so the distance it drove is 50 mph x 2 hours = 100 miles.

Finally, the total distance the tourist has to pay the taxi driver is the sum of the distance the tourist walked and the distance the taxi drove, or 8 miles + 100 miles = 108 miles.

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Complete question:

A tour begins walking along a 31-mile road to a mountain summit. He travels at a rate of 4 mph. After a while, he gets tired and calls a taxi. The taxi, traveling at a constant ped of 50 mph reached his destination 2 hours after he started walking, what distance doe he have to pay the taxi driver

There are 60 blue tiles, 80 red tiles, and 160 white tiles in the bathroom pattern

Let's call the number of individual tiles "x".

Using the given ratio, we have

Then there are 3x blue tiles, 4x red tiles and 8x white tiles.

The total number of tiles is:

3x + 4x + 8x = 300

Evaluate the like terms

15x = 300

Dividing both sides by 15

x = 300 / 15 = 20

So, we have

Blue = 3 * 20 = 60

Red - 4 * 20 = 80

White = 8 * 20 = 160

So there are 60 blue tiles, 80 red tiles, and 160 white tiles.

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2084 is the total number of integers between 4000 and 4999 with at least one repeated digit.

An integer is a whole number, which can be positive, negative, or zero. A repeated digit refers to a digit that appears more than once in the number.

First, let's count the number of integers between 4000 and 4999 that have no repeated digits. We have 4 choices for the thousands place, as it must be 4. For each of the remaining three places, we have 9 choices for digits (0 to 9, except for 4 in the thousands place). So, the total number of integers between 4000 and 4999 with no repeated digits is 4 * 9 * 9 * 9 = 2916.

Next, we need to count the number of integers with one repeated digit. For this, we need to consider two cases:

When the repeated digit is in the thousands place. In this case, there are only 9 choices for the other three digits, as they cannot be 4. The total number of integers in this case is 9 * 9 * 9 = 729.

When the repeated digit is not in the thousands place. In this case, there are 9 choices for the repeated digit and 8 choices for the other two digits. So, the total number of integers in this case is 9 * 9 * 8 = 648.

Adding the total number of integers in both cases, we get 729 + 648 = 1377 integers between 4000 and 4999 with at least one repeated digit.

Finally, subtracting the number of integers with no repeated digits from the total number of integers between 4000 and 4999, we get 5000 - 2916 = 2084. This is the total number of integers between 4000 and 4999 with at least one repeated digit.

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By applying exponential decay concept, it can be concluded that the exponential equation to model the value of the snowmobile is A = 500 · 0.85ⁿ where n is the times (in years).

Exponential decay occurs when the amount of something decreases at a rate proportional to the amount left.

A = P (1 - r)ⁿ   where:

A = final amount

P = initial amount

r = decay factor

n = time

We have the following information:

P = $500

r = 15%

The exponential equation to model the value of the snowmobile can be written as follows:

A = P (1 - r)ⁿ

A = 500 (1 - 15%)ⁿ

A = 500 · 0.85ⁿ

Thus, the exponential equation to model the value of the snowmobile is A = 500 · 0.85ⁿ where n is the times (in years).

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Answer:

C. 12,000(1.05)^n < 20,000

Step-by-step explanation:

A = P(1 + r)^t

P = $12,000

r = $5 dollar per year

t = n years

$12,000(1 + 5/100)^n

$12,000(1 + 0.05)^n

$12,000(1.05)^n

The question states, "The tuition is less than 20,000", therefore:

[$12,000(1.05)^n < 20,000]

The number line of y < 1/2 is repesented below

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

y < 1/2

A number line represents all real numbers on a line and is usually represented as a horizontal line with numbers increasing from left to right.

The symbol "<" in the equation y < 1/2 means "less than."

So, all values of y that are less than 1/2 would be graphed to the left of 1/2 on the number line.

The number line would look like this:

   -1.0         -0.5           0.0         0.5         1.0

   ____________|______________|____________|____________

    y < 1/2                                 1/2

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There were 70 Republicans and 84 Democrats in the state senate.

Let x be the number of Republicans in the state senate.

Then the number of Democrats is x + 14.

We know the ratio of Democrats to Republicans is 6 to 5.

According to the given conditions, we can write the equation as follows -

x / (x + 14) = 5 / 6

Cross multiplying, we get,

6x = 5x + 70

Subtracting 5x from both sides of the equation, we get,

x = 70

Therefore, we get that there were 70 Republicans and 84 Democrats in the state senate.

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I am sorry but I cannot answer your question with the contained elements.

In analytical geometry, a y-intercept, also known as a vertical intercept, is the point where the graph of a function or relation intersects the y-axis of the coordinate system using the widely accepted convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Therefore, x = 0 is satisfied at these sites.

y = -3+1

2y = 4x + 2

y = 22 +3

+y = 3

S y = 3x + 4

y=x+4

y = x - 1

2 = 2x - 2

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By definite integrals, we find that the area of the region bounded by the functions f(x) and g(x) described in the statement is equal to 4.5 units.

In this problem we must determine the area between two functions, a quadratic equation f(x) and a linear equation g(x).

First, we need to determine the limits of the interval of x-values with the help of a graphing tool, represented by the points of intersection of the two functions.

The points of intersection of the two functions are (x₁, y₁) = (- 5, 4) and (x₂, y₂) = (- 2, 1), respectively. Then, the area is defined by the following definite integral:

[tex]I=\int_{-5}^{-2}[g(x)-f(x)]dx\\\\I=\int_{-5}^{-2}(-x-1)-(x+3)^2]dx\\\\I=4.5 unit^2[/tex]

The area of the region represented by the definite integral introduced above is equal to 4.5 units.

The complete question is -

Find the area of the region that is bounded above by the curve f(x) = (x + 3)² and the line g(x) = - x - 1 and bound above the x-axis.

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The equation cannot be solve using substitution

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

-5(-2)x−4y=−10

The above equation is a lone equation

For an equation to be solved using substitution, there must be at least two equations

Hence, the equation has no solution

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Answer:

$69.

Step-by-step explanation:

he store marked up the silver coat rack for $48 * 25/100 = $12.

So the silver coat rack was sold for $48 + $12 = $60.

The sales tax is $60 * 15/100 = $9.

Thus, Prithia paid a total of $60 + $9 = $69.

Elena receives a higher value per hour, she earns $16.8 more than Jada.

A unit rate means a rate for one of something.

Given that, Elena's earning can be given by, y = 8.40x where x represents how many hours she works and y represents how much money she earns. And Jada earns $7 per hour

We need to calculate the total income for 12 hours:

Therefore,

For Elena =

y = 8.40 x 12

y = $100.8

For Jada =

y = 7 x 12

y = $84

Thus, $100.8 - $84 = $16.8

Hence, Elena receives a higher value per hour, she earns $16.8 more than Jada.

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The maximum compression of the spring will depend on the spring's elasticity, or its ability to return to its original length after being stretched or compressed which is 2cm

If the same puck hits the spring at a speed of 2v, the spring will compress twice as much as it did when the puck was traveling at v. Thus, the spring's maximum compression will be 2 cm or twice its original compression of 1 cm.

It is important to note that the spring's elasticity will affect the maximum compression. If the spring is relatively stiff and has a low elasticity, it will not compress as far as a spring with a higher elasticity.

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The complete question should be: A hockey puck sliding along frictionless ice with speed v to the right collides with a horizontal spring and compresses it by 1.0 cm before coming to a momentary stop. What will be the spring's maximum compression if the same puck hits it at a speed of 2v?

Answer:

37° and 63°

Step-by-step explanation:

the measure of a secant- secant angle and a tangent- tangent angle is half the measure of the intercepted arcs.

5

∠ 1 = [tex]\frac{1}{2}[/tex] (108 - 34)° = [tex]\frac{1}{2}[/tex] × 74° = 37°

6

the sum of the arcs in a circle is 360° , then

minor arc = 360° - 243° = 117°

∠ 1 = [tex]\frac{1}{2}[/tex] (243 - 117)° = [tex]\frac{1}{2}[/tex] × 126° = 63°