Answer:16
Step-by-step explanation:
NEED THIS DESPERATELY !! PLEASE HELP
Answer:222
Step-by-step explanation:The arithmetic series is given by:
a1 = 2, d=3, n = 12
where a1 is the first term, d is the common difference, and n is the number of terms.
To evaluate this series, we can use the formula for the sum of an arithmetic series:
Sn = n/2 * [2a1 + (n-1)d]
where Sn is the sum of the first n terms.
Substituting the given values, we get:
S12 = 12/2 * [2(2) + (12-1)(3)]
= 6 * [4 + 33]
= 6 * 37
= 222
Therefore, the sum of the first 12 terms of the arithmetic series with a1 = 2, d=3 is 222.
what is the meaning of the following statement?
The proposition states that if the multiplication operation in a set is commutative and associative, then the product of any sequence of elements in the set, arranged according to any permutation of the sequence, will be the same as the product of the elements arranged in their original sequence.
What is associative multiplication and permutation?Associative multiplication refers to a property of multiplication where the order of performing the multiplication does not affect the final result. In other words, if we have three elements a, b, and c, then (a x b) x c is equal to a x (b x c).
Permutation refers to the rearrangement of a set of elements in a specific order. In mathematics, a permutation of a set of n elements is a bijective function from the set of integers {1,2, ..., n} to itself. In other words, a permutation is a way of rearranging the elements of a set in a specific order by swapping them around.
In the context of the given proposition, the associative property of multiplication ensures that the order of multiplication of elements in the product Xσ(1) Xσ(2) ... Xσ(n) can be rearranged without changing the final result. The proposition states that no matter how we permute the order of multiplication of elements, the final product will be the same, provided that the multiplication operation is both commutative and associative.
In other words, if we have a set of elements X1, X2, ..., Xn, and we multiply them together using a commutative and associative multiplication operation, then no matter how we permute the elements (i.e., rearrange them in a different order), the result of the multiplication will be the same.
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Consider the given function.
ƒ(1): =
5,
I < -2
3, -2 <=<0
0,
0 <=<2
> 2
-3,
Which graph represents the given function?
Help
Please …….
Zxrxrxrdrdrxxtxtcvyhnin
The box-and-whisker plot shows that the dataset has a median of approximately 5.5 and is relatively symmetric, with the middle 50% of the data falling between approximately 4 and 7.
The box-and-whisker plot offers a visual summary of the distribution of the given dataset. The following is one way to understand the plot:
The median, which is the midway number when the data is organised from least to largest, is shown by the line inside the box. The median in this situation is roughly 5.5.
The box's bottom edge corresponds to the first quartile (Q1) and its top edge to the third quartile, and it represents the middle 50% of the data (Q3). The interquartile range is the space between Q1 and Q3 (IQR). In this instance, Q1 is roughly 4 and Q3 is roughly 7, hence the IQR is roughly 3.
The whiskers reach from the box's boundaries to the dataset's lowest and largest values that aren't regarded as outliers. Although there are many different definitions of an outlier, it is generally accepted that any number that is more than 1.5 times the IQR below Q1 or above Q3 qualifies as an outlier. There aren't any anomalies in this circumstance.
Individual data points outside the box and whiskers are shown as dots above and below the whiskers. There are no such data points in this situation.
Hence, the box-and-whisker plot reveals that the dataset is very symmetrical and has a median of about 5.5, with the middle 50% of the data ranging between roughly 4 and 7.
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Simplify the given expression, and most importantly show the steps, please.
Answer:
[tex]\frac{3\sqrt{2} }{2}[/tex]
Step-by-step explanation:
[tex]\frac{6}{\sqrt{8} } =\frac{6}{\sqrt{4*2} } =\frac{6}{\sqrt{4}*\sqrt{2} }=\frac{6}{2*\sqrt{2} }= \frac{3}{\sqrt{2} }[/tex]
I simplified it leaving 3/sqrt(2).
We can not leave the denominator sqrt(2) for some reason due to a rule that i forgot.
[tex]\frac{3}{\sqrt{2} }*\frac{\sqrt{2} }{\sqrt{2} } =\frac{3*\sqrt{2} }{\sqrt{2}* \sqrt{2} } =\frac{3\sqrt{2} }{(\sqrt{2})^2 } =\frac{3\sqrt{2} }{2}[/tex]
Answer:
[tex]\dfrac{3\sqrt{2}}{2}[/tex]
Step-by-step explanation:
To simplify the given rational expression, first rewrite 8 as a product of prime numbers.
[tex]\implies \sf 8 = 2 \cdot 2 \cdot 2[/tex]
As we know that [tex]\sqrt{a^2}=a[/tex], rewrite 8 as 2² · 2:
[tex]\implies \dfrac{6}{\sqrt{2^2 \cdot 2}}[/tex]
[tex]\textsf{Apply radical the rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
[tex]\implies \dfrac{6}{\sqrt{2^2} \sqrt{2}}[/tex]
[tex]\textsf{Apply radical the rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies \dfrac{6}{2\sqrt{2}}[/tex]
Rewrite 6 as a product of prime numbers:
[tex]\implies \dfrac{2 \cdot 3}{2\sqrt{2}}[/tex]
Cancel the common factor 2:
[tex]\implies \dfrac{\diagup\!\!\!\!2 \cdot 3}{\diagup\!\!\!\!2\sqrt{2}}=\dfrac{3}{\sqrt{2}}[/tex]
For a fraction to be in simplest form, the denominator should not be irrational.
To rationalize the denominator (get rid of the radical in the denominator), multiply the numerator and denominator by the radical of the denominator:
[tex]\implies \dfrac{3}{\sqrt{2}} \cdot \dfrac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\implies \dfrac{3\sqrt{2}}{\sqrt{2}\sqrt{2}}[/tex]
[tex]\textsf{Apply radical the rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]
[tex]\implies \dfrac{3\sqrt{2}}{\sqrt{2 \cdot 2}}[/tex]
[tex]\implies \dfrac{3\sqrt{2}}{\sqrt{2^2}}[/tex]
[tex]\textsf{Apply radical the rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies \dfrac{3\sqrt{2}}{2}[/tex]
Coach Walker has a cooler that can hold 5 1/2 gallons of a sports drink. He fills 3/4 of
the cooler with the sports drink to bring to football practice.
A. How many gallons of the sports drink did Coach Walker put into the cooler? Each
player on the football team fills his water bottle with the sports drink from the
cooler. Each water bottle can hold 1 1/2 pints of the sports drink. (1 gallon = 8 pints)
Show your work or explain how you know.
The gallons of the sports drink that Coach Walker put in the cooler is 4 1/8 gallons.
How many gallons were put in the cooler?In order to determine the gallons of the sports drink that was put into the cooler, multiply 5 1/2 by 3/4.
Multiplication is the process of determining the product of two or more numbers. The sign that is used to denote multiplication is x.
Gallons of sports drink that was put into the cooler = 5 1/2 x 3/4
= 11/2 x 3/4 = 33 / 8 = 4 1/8 gallons
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Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is lower than that of the general population.
(a) State the hypotheses that we can use to consider this question.
(b) Carry out the hypothesis test in (a) using the critical-value method with a significance level of .05, and summarize your findings.
(c) What is the p-value for the test conducted in (b)?
(d) The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether the standard deviation from the low-income group is lower than that of the general population. State the hypotheses that we can use to answer this question.
(e) Carry out the test in (d) and report the p-value with an α level of .05, and summarize your findings.
Answer:
The null hypothesis is that the mean daily iron intake of the low-income group is equal to or greater than the general population, and the alternative hypothesis is that the mean daily iron intake of the low-income group is less than that of the general population.
H0: μ >= 14.44
Ha: μ < 14.44
(b) We can use a one-tailed t-test to test this hypothesis. With a sample size of 51, degrees of freedom of 50, a sample mean of 12.50, a population mean of 14.44, and a standard deviation of 4.75, we can calculate the t-statistic as follows:
t = (12.50 - 14.44) / (4.75 / sqrt(51)) = -3.16
Using a t-distribution table with 50 degrees of freedom and a significance level of .05, the critical value is -1.677. Since the calculated t-statistic is less than the critical value, we reject the null hypothesis.
Therefore, we can conclude that the mean daily iron intake among the low-income group is significantly lower than that of the general population at a significance level of .05.
(c) The p-value for this test is the probability of obtaining a t-value of -3.16 or more extreme assuming the null hypothesis is true. Using a t-distribution table with 50 degrees of freedom, we find the p-value to be less than .005.
(d) The null hypothesis is that the standard deviation of the low-income group is equal to or greater than that of the general population, and the alternative hypothesis is that the standard deviation of the low-income group is less than that of the general population.
H0: σ >= 5.56
Ha: σ < 5.56
(e) We can use a chi-square test to test this hypothesis. With a sample size of 51, degrees of freedom of 50, and a sample standard deviation of 4.75, we can calculate the chi-square statistic as follows:
chi-square = (n - 1) * s^2 / σ^2 = 50 * 4.75^2 / 5.56^2 = 39.70
Using a chi-square distribution table with 50 degrees of freedom and a significance level of .05, the critical value is 68.67. Since the calculated chi-square statistic is less than the critical value, we fail to reject the null hypothesis.
Therefore, we do not have sufficient evidence to conclude that the standard deviation of daily iron intake among the low-income group is significantly lower than that of the general population at a significance level of .05.
Eudora ran from her home to her secret laboratory at an average speed of
12
km/h
12 km/h12, start text, space, k, m, slash, h, end text. She then took one of her jetpacks and flew to her school at an average speed of
76
km/h
76 km/h76, start text, space, k, m, slash, h, end text. Eudora traveled a total distance of
120
120120 kilometers, and the entire trip took
2
22 hours.
How long did Eudora spend running, and how long did she spend flying using her jetpack?
Eudora spent 0 hours running and 2 hours flying using her jetpack.
Let's use the formula: time = distance / speed.
Let x be the time Eudora spent running and y be the time she spent flying using her jetpack.
From the problem, we know that:
Eudora ran at an average speed of 12 km/h, so she covered a distance of 12x kilometers while running.
Eudora flew at an average speed of 76 km/h, so she covered a distance of 76y kilometers while flying.
The total distance she traveled was 120 kilometers, so: 12x + 76y = 120.
The entire trip took 2 hours, so: x + y = 2.
We can use the second equation to solve for x: x = 2 - y.
Substituting into the first equation, we get: 12(2 - y) + 76y = 120.
Simplifying the equation, we get: 152 - 64y = 120.
Solving for y, we get: y = 2 hours.
Substituting into x = 2 - y, we get: x = 0 hours.
Therefore, Eudora spent 0 hours running and 2 hours flying using her jetpack.
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Complete question:
Eudora ran from her home to her secret laboratory at an average speed of 12 km/h. She then took one of her jetpacks and flew to her school at an average speed of 76 km/h. Eudora traveled a total distance of 120 kilometers, and the entire trip took 2 hours.
How long did Eudora spend running, and how long did she spend flying using her jetpack?
What is the volume of this rectangular prism?
A)40 cu in
B)120 cu in
C)22cu in
D)84 cu in
Answer: B (120 in^3)
Step-by-step explanation: W * L *H = V
Length * Width * Height = Volume
You can multiply the LWH in any order.
Height = 4
Length = 10
Width = 3
Remember, anything multiplied by ten is just the product (answer) with a zero added to the end. Example: 4 * 3 = 12; 12 * 10 = 120
Another Example: 15 * 2 = 30; 30 * 10 = 300
4 * 10 = 40
40 * 3 = 120
Therefore, 120 is your answer.
Hope this helps!
Answer:
The answer to your problem is, 120 cu in
Step-by-step explanation:
In order to find the volume of the cube there is only one thing that you need to do which is pretty simple just follow these steps:
Multiply, l * w * h ( * = multiply )
By following the formula up above you can find the volume of a rectagular prism which is:
4 x 10 = 40
3 x 40 = 120.
Thus the answer to you problem is, 120 cu in
i need to graph y=-1/4x+6
Answer:y intercept is 6 slope is -1/4
Step-by-step explanation:
to graph it in y=mx+b form b is the y intercpt and where you start the graph and m is the slope is [tex]-\frac{1}{4}[/tex] the you go to the right 4 and up one to graph the line
203,433 rounded to the nearest ten thousand
Step-by-step explanation:
203,433 rounded to the nearest ten thousand is 200,000.
Which sequence of transformations results in figures that are similar but not congruent
Answer:
When two shapes are similar but not congruent, the sequence of steps showing the similarity usually has a single dilation and then the rest of the steps are rigid transformations. The dilation can come at any time.
Step-by-step explanation:
When two shapes are similar but not congruent, the sequence of steps showing the similarity usually has a single dilation and then the rest of the steps are rigid transformations. The dilation can come at any time.
A payday loan is made for four weeks, where the amount of interest owed per $100
borrowed is $10
. If you borrow $800
for four weeks, how much do you owe at the end of the four weeks?
Converting Standard Form-Slope Intercept Form
Solve for y.
Step 1: Move the x term to the other
side by performing the opposite
operation to BOTH sides.
-7x+y=-17
+ [?];
+7x
Therefore , the solution of the given problem of slope comes out to be y = 7x - 17 is the equation in slope-intercept form.
Explain slope.A line's steepness is determined by its slope. In gradient-based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).
Here,
Given :
=> -7x + y = -17
7x both faces together
=> -7x + 7x + y = 7x - 17
Condense: y = 7x - 17
So,
=> y = 7x - 17 is the equation in slope-intercept form.
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•Taylorann Johnson 3/6/23 3td pero For each parabola, label all parts on the curve. Circle if it is a max or a min. Fill in the points or lines. 1 Name 1. y = x² Opens up or down? Positive Vertex (0.0) Max/Min Axis of Symmetry: x=__ y-intercept (,0) x-intercept(s) or the zeros ( ) [ Parabola Review Domain: (0₁2) Range: (1,8)
For the given parabola, the parts on the curve should be labeled as follows;
The parabola with the equation y = x² opens up.The vertex of the parabola are (0, 0).The max/min value are equal to (0, 0).The axis of symmetry is x = 0.The y-intercept is equal to (0, 0).The x-intercept or the zeros is (0, 0).The domain is equal to (-∞, ∞).The range is equal to (0, ∞).How to calculate the vertex and axis of symmetry of a quadratic function?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using the following mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = y = x², we have the following:
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(0)/2(1)
Axis of symmetry, Xmax = 0/1 = 0.
Vertex (h, k) = (0, 0).
In conclusion, the domain of this quadratic function f(x) = y = x² are all the x-values that are located on the x-axis of the graph, which include {-∞, ∞} or all real numbers.
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Find the equation of the line that passes through the given point and has the given slope. ( Use x as your variable.) (- 9, - 9), m = 0
An equation of the line that passes through the given point and has the given slope is y = -9.
What is the point-slope form?In Mathematics, the point-slope form of any straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represent the points.At data point (9, -9) and slope, m = 0, a linear equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - (-9) = 0(x - 9)
y + 9 = 0
y = -9
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Which relationships describe angles 1 and 2?
Select each correct answer.
A. supplementary angles
B. complementary angles
C. vertical angles
D. adjacent angles
The relationship which describe angles 1 and 2 is supplementary angles.
The correct answer choice is option A.
What are supplementary angles?Supplementary angles are angles in which the sum of their measure is equal to 180°.
Based on this, angles 1 and 2 are supplementary because they both add up to 180°.
Complementary angles are two angles which add up to 90 degrees.
Vertical angles are angles opposite each other when two angles intersect.
Adjacent angles are angles which have a common side and common vertex.
Hence, angles 1 and 2 are supplementary.
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Can someone please help
The value of the variable x is 8. 25
How to determine the value of the variableIt is important to know the properties of a kite. They are;
It has two pairs of adjacent equal sidesIt has one pair of opposite angles that are equal to each otherThe shorter diagonal forms two isosceles trianglesThe longer diagonal forms two congruent trianglesAlso, the diagonals are perpendicular to each otherNote that the sum of the interior angles of a triangle is equal to 180 degrees
So,
m<R + m< V + m< S = 180
substitute the values
9x + 1 + 90 + 23x - 7 = 180
collect like terms
32x = 180 + 84
32x = 264
x = 8. 25
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Write the six trig functions for the following
SOH CAH TOA
Please and thank you
The six trig functions are:
(1) Figure 1, sin θ = 1/√5
(2) Figure 1, cos θ = 2/√5
(3) Figure 1, tan θ = 1/2
(4) Figure 2, sin θ = 3/√13
(5) Figure 2, cos θ = 2/√13
(6) Figure 2, tan θ = 3/2
What is a trig function?Trig function (short for "trigonometric function") is a mathematical function that relates the angles of a right triangle to the lengths of its sides. The main trig functions are sine (sin), cosine (cos), and tangent (tan).
The trig functions are abbreviated using SOH CAH TOA.
SOH : sin θ = opposite / hypotheses
CAH: cos θ = adjacent / hypothenuse
TOA : tan θ = opposite / adjacent
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The rate of change of the angle of elevation is 0.00011 rad/ft, for that we have to know the elevation.
What is Elevation?The height above or below a specified(predefined) reference point, most frequently a reference geoid, which is a mathematical representation (expression) of the Earth's sea level as an equipotential gravitational surface, determines(defines) a location's elevation.
The angle of elevation of the camera is, Θ= [tex]tan^-^1(\frac{x}{2000} )[/tex]
The distance between the camera and the launching pad is, b= 2000 ft
The distance between the camera and the racket is, h = 4255 ft
To find the rate of change of the angle of elevation of the camera, we need to differentiate the function of that angle.
Θ= [tex]tan^-^1(\frac{x}{2000} )[/tex]
Differentiating function with respect to x we have,
[tex]\frac{d}{dx}[/tex] Θ=[tex]\frac{d}{dx} tan^-^1(\frac{x}{2000} )[/tex]
Θ'=[tex]\frac{1}{1+\frac{x^2}{2000^2} }[/tex][tex]*\frac{1}{2000}[/tex]
[tex]\frac{1}{2000+\frac{x^2}{2000} }[/tex] (Equation 1)
[tex]h^2=b^2+p^2[/tex]
[tex]4255^2+2000^2+x^2[/tex]
Θ=[tex]\frac{1}{2000+\frac{14105025}{2000} }[/tex]
≈ 0.00011 rad/ft.
Thus, the rate of change of the angle of elevation is 0.00011 rad/ft.
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i’m confused on this
The value of the side x is 8. 4
How to determine the value of the variableIt is important to note that the Pythagorean theorem states that the square of the longest leg of a triangle, is equal to the sum of the squares of the other two sides, that is, the opposite and adjacent sides.
The formula is expressed as;
a² = b² + c²
From the information shown in the diagram, we have that;
Hypotenuse side = 21
Adjacent side = 12. 6
Opposite side = 2(x)
Substitute the values
x² = 21² - 12.6²
find the squares
x² = 441 - 158. 76
subtract the values
x = 16. 8
But, we have that this value is the diameter but x as shown is the radius.
Radius, x = 16. 8 /2 = 8. 4
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Please answer the question in the picture, I will mark brainliest. Show all work pls!!!
Arc length= 2pir * zero with a circle through it/360
Just for clarification 2pir is 2 then pi then r together
.72 radians is the answer.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
The relation of the arc length of a circle subtended by an angle to the radius of the circle is the definition of an angle in radians.
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describe javiers works by ritting an divison equationthat includes a fraction
thats part a the real question jevier drew a model to determine how many fifths are in 6 wholes
After addressing the issue at hand, we can state that Javier's model equation predicts that there are 30 fifths in 6 wholes.
What is equation?A mathematical statement known as an equation demonstrates the equivalence of two expressions when they are joined by the equals sign ('='). As an illustration, 2x - 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' joins the two expressions together. An equation is a mathematical formula with two algebraic expressions on either side of the equal sign (=). It shows how the left and right formulas have an equivalent relationship. In any formula, L.H.S. = R.H.S. (left side = right side).
To describe Javier's work, one division equation with a fraction might be written as follows:
6 ÷ (1/5) =
How many fifths are there in six wholes? is the equation that illustrates the question Javier was attempting to answer. In order to answer this equation, we must divide 6 by the fraction 1/5, which is equivalent to multiplying 6 by 1/5's inverse, or 5/1:
6 ÷ (1/5) = 6 × (5/1) = 30
Javier's model predicts that there are 30 fifths in 6 wholes.
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a) What is the height of the container if it’s a cylinder with a radius of 3cm?
b) If the container from Part A is filled with coffee and coffee costs $0.02 per cubic centimeter, what is the cost of coffee?
a. The Vοlume = 198 cm³ and height = 7, if it’s a cylinder with a radius οf 3cm.
b. The cοst οf cοffee is $3.96 when $0.02 per cubic centimetre.
What is the fοrmula fοr the vοlume οf the cylinder?The fοrmula fοr the vοlume οf a cylinder is
V = πr²h,
where V is the vοlume, r is the radius, and h is the height.
a) Tο find the height οf the cylinder, we need tο knοw the vοlume οf the cοntainer and the radius. The fοrmula fοr the vοlume οf a cylinder is:
V = πr²h
[tex]$\mathrm{\frac{V }{ h}} = \pi r\² }[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{22}{7} \times 3 \times 3}[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{22}{7} \times 3 \times 3}[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{198}{7}[/tex]
Thus, Vοlume = 198 cm³ and height = 7
b) If the cοntainer frοm is filled with cοffee and cοffee cοsts $0.02 per cubic centimetre, Then the cοst οf cοffee
= $0.02 × 198 cm³
= $3.96
Thus, The Vοlume = 198 cm³ and height = 7, if it’s a cylinder with a radius οf 3cm.
The cοst οf cοffee is $3.96 when $0.02 per cubic centimetre.
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please help me..........................
In response to the given question, we can state that So the entire function factored expression is: 8x + 96y = 8(x + 12y)
what is function?Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.
To factor 8x + 96y, we can first factor out the greatest common factor, which is 8.
8x + 96y = 8(x + 12y)
So the entire factored expression is:
8x + 96y = 8(x + 12y)
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An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the linear regression line for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
Number of TV commercials, x 4
6
12
14
17
Car sales, y (in hundreds) 2
5
2
8
9
Answer:
the linear regression line for the given data is: y = 0.24x + 2.49
Step-by-step explanation:
To find the linear regression line for the given data, we need to first calculate the mean of x, the mean of y, the sum of squares of x, the sum of squares of y, and the sum of cross-products of x and y.
Using these values, we can then calculate the slope and y-intercept of the regression line.
First, we calculate the mean of x and y:
mean of x = (4 + 6 + 12 + 14 + 17) / 5 = 10.6
mean of y = (2 + 5 + 2 + 8 + 9) / 5 = 5.2
Next, we calculate the sum of squares of x and y:
sum of squares of x = (4 - 10.6)^2 + (6 - 10.6)^2 + (12 - 10.6)^2 + (14 - 10.6)^2 + (17 - 10.6)^2 = 240.4
sum of squares of y = (2 - 5.2)^2 + (5 - 5.2)^2 + (2 - 5.2)^2 + (8 - 5.2)^2 + (9 - 5.2)^2 = 44.8
Finally, we calculate the sum of cross-products of x and y:
sum of cross-products of x and y = (4 - 10.6)(2 - 5.2) + (6 - 10.6)(5 - 5.2) + (12 - 10.6)(2 - 5.2) + (14 - 10.6)(8 - 5.2) + (17 - 10.6)(9 - 5.2) = 56.8
Using these values, we can calculate the slope of the regression line:
slope = sum of cross-products of x and y / sum of squares of x = 56.8 / 240.4 = 0.236
Next, we can calculate the y-intercept of the regression line:
y-intercept = mean of y - slope * mean of x = 5.2 - 0.236 * 10.6 = 2.488
Therefore, the linear regression line for the given data is:
y = 0.24x + 2.49
Note: The slope and y-intercept have been rounded to two decimal places, as per the instructions.
Find the equilibrium level of national income in the basic Keynesian macroeconomic model
Y=c+I
C= 40+ 0.5y
I= 200
Therefore, the equilibrium level of national income in this basic Keynesian macroeconomic model is 480.
What is sum?In mathematics, the sum is the result of adding two or more numbers or quantities together. The symbol used to represent a sum is the capital Greek letter sigma (∑), which stands for "sum up."
by the question.
In the basic Keynesian macroeconomic model, equilibrium occurs when national income (Y) equals total spending in the economy. Therefore, we can set Y equal to the sum of consumption (C) and investment (I), as follows:
Y = C + I
Substituting the given consumption and investment functions into this equation, we get:
Y = (40 + 0.5Y) + 200
Simplifying and rearranging, we get:
Y - 0.5Y = 240
0.5Y = 240
Y = 480
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Select from the drop-down menu to correctly complete each comparison 4.408
The prοduct οf the matrices is nοt the identity matrix. Therefοre, X and A nοt inverses οf each οther.
What is an identity matrix?An identity matrix is a square matrix in which all the elements οf principal diagοnals are οne, and all οther elements are zerοs. It is denοted by the nοtatiοn “In” οr simply “I”. Any matrix will yield a matrix as a result of being multiplied by the identity matrix.
The identity matrix is a matrix having entry οne in its diagοnal and rest οf the entries are zerο.
[tex]X.A = \left[\begin{array}{cc}2&-1\\6&-4\\\end{array}\right] \left[\begin{array}{cc}1/2&1/4&\\-2&-1/2&\end{array}\right][/tex]
[tex]X.A = \left[\begin{array}{cc}3&1\\11&7/2\end{array}\right][/tex]
Hence, The prοduct of the matrices is not the identity matrix. Therefοre, X and A not inverses of each other.
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The complete question is in the attached image.
A bakery sells chocolate cupcakes and mocha cupcakes. One day it sold 162 chocolate and 138 mocha. What percent of the cupcakes sold that day were chocolate?
Answer:
54%Step-by-step explanation:
TOTAL CUPCAKES
162+138=300
[tex] \frac{162}{300} \times 100\% \\ = 54\%[/tex]
23841.0596 in standard form
Answer:
23841.0596 in standard form is 2.38410596 x 10^4.
Step-by-step explanation:
Answer:
2.38410596 x 10^4
Step-by-step explanation:
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