The relationship between the price of the cap and the number of units in demand is d = 869 - 19p
What is Substitution?Substitution: A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable.
The table below shows survey results for the demand related to the price of a baseball cap in a small town. As the price of the cap increases, the number of people who wish to purchase it decreases.
Price of Cap, p(in dollars) Number of Units in Demand, d
23 432
27 356
30 299
35 204
the relationship between the price of the cap and the number of units in demand
lets substitute the values in the given options ( lets use 1st result p=23 and d=432)
A.
d = 850 - 19p
432=850-19(23)
432=850-437
432≠413
B.
d = 285 - 869p
432=285-869(23)
432=285-19,987
432≠19,702
C.
d = 869 - 19p
432=869-19(23)
432=869-437
432=432
option C is correct
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A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable.
The table below shows survey results for the demand related to the price of a baseball cap in a small town. As the price of the cap increases, the number of people who wish to purchase it decreases.
The relationship between the price of the cap and the number of units in demand
lets substitute the values in the given options ( lets use 1st result p=23 and d=432)
A. d = 850 - 19p
432=850-19(23)
432=850-437
432≠413
B. d = 285 - 869p
432=285-869(23)
432=285-19,987
432≠19,702
C. d = 869 - 19p
432=869-19(23)
432=869-437
432=432
Leah runs M miles everyday during the week except for Wednesday or Sunday. A. write an algebraic expression that represents the total number of miles leah runs each week B. there are 52 weeks in a year. write an algebraic expression that represents the total number of miles leah runs in a year
A. The algebraic expression that represents the total number of miles Leah runs each week is 5*M.
B. The algebraic expression that represents the total number of miles Leah runs in a year is 260*M.
Leah runs M miles everyday during the week except for Wednesday or Sunday.
We need to write the algebraic expression that represents the total number of miles Leah runs each week. Leah runs for 5 days in a week. The total number of miles run in a week is 5*M.
We need to write the algebraic expression that represents the total number of miles Leah runs in a year. Leah runs 5*M miles in a week. The total number of miles run in a year is (5*M)*52 = 260*M.
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Justin is playing tennis. When serving, he stands 12 feet away from the net, which is 3 feet tall. The ball is served from a height of 7.5 feet. Justin thinks the ball travels about 21.4 feet before it hits the ground 8 feet from the net on the opposite side.
a) How far does the ball travel?
b) What assumptions did you make to solve the distance the ball travels?
c) What mathematical practice did you use to solve this problem?
Regarding the situation described, we have that:
a. The ball travels 21.4 feet.
b. The assumption is that the ball was served at an angle of 90º.
c. The Pythagorean Theorem was used to solve this problem.
Pythagorean TheoremThe Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, it is found that:
The vertical change in the height of the ball was of 7.5 feet, as it was served from a height of 7.5 and hit the ground.The horizontal change in the height of the ball is of 12 + 8 = 20 feet, as he served 12 feet from the net, and the ball hit the ground 8 feet from the net on the opposite side.Assuming that the ball was served at an angle of 90º, the distance traveled by the ball is the hypotenuse of a right triangle of legs 7.5 feet and 20 feet, hence:
d² = 7.5² + 20².
d = sqrt(20² + 7.5²)
d = 21.4 feet. (which is Justin's estimate).
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what is 5/3x +1/3 = 13/1/3 + 8/3x
Answer: x = − 116/3
Step-by-step explanation:
Evaluate 5/3x + 1/3 = 13/1/3 +8/3x
Multiply the numbers 5x/3 + 1/3 = 13/1/3 + 8/3x
Simplify 5x/3 + 1/3 = 39 + 8x/3
Multiply both sides 5x/3 × 3 + 1/3 × 3 = 39 × 3+ 8/3x × 3
Simplify the expression 5x+1=117+8x
Move the variable to the left side 5x+1−8x=117
Subtract the terms −3x+1=117
Move the constant to the right side −3x=117−1
Subtract the terms −3x=116
Divide both sides −3x/-3 = 116/-3
Simplify −3x/-3 = 116/-3
Solution x = − 116/3
What is the number in standard form?
QUESTION:
5.8×10−10
Options:
A.0.00000000088
B.0.00000000005008
C.0.0000508
D.0.00000005008
E.0.0000000508
F.0.0000058
5.8×10^-10 in standard form is: 0.00000000058.
What is standard form?Standard form can be defined as the way of written a number of digit in a simple form for easy understanding.
Given data:
5.8 × 10 ^ -10
Now let this scientific notation 5.8 × 10 ^-10 into a standard form.
We know that 5.8×10^-10 can be re-written as :
5.8 ÷ 10 ^-10
= 5.8 × 10×10×10×10×10×10×10×10×10×10
= 5.8 ÷ 10000000000
= 0.00000000058
Hence,
5.8×10^-10 = 0.00000000058
Therefore we can conclude that 0.00000000058 is the standard form of 5.8 ×10 ^-10.
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A store owner mixes 2 Ib of candy that costs x dollars per pound with 3 Ib of candy that costs $1.50 per pound. She sells the mix for $2.50 per pound.
The 2lb candy cost the owner $8 and the 3lb candy cost the owner $4.5
What is the cost of 2lb candyThe total weight of the candy is
[tex]3 + 2 = 5[/tex]
Let's write equation for this.
[tex]3(1.50) + 2x = 2.5(5)\\4.5 + 2x = 12.5\\12.5 - 4.5 = 2x \\8 = 2x\\x = 4[/tex]
The cost of the 2 pound candy is $4 per unit and the store owner spent $8 in the 2lb candy.
The cost of 3 pound candy was $4.5
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I need to show a picture of the problem
x and y intercepts are the points where lines cut off the x and the y axis respectively.
In this case, the line cuts the x axis at x=-8. It means that the x intercept of the line is (-8,0).
The line also cuts the y axis at y=-6, which means that the y intercept of the line is (0,-6).
20. If the measure of angle 5 = x, which angles have a measure of 180 - x? Select all that apply.
(A) angle 2
B angle 3
C) angle 7
D angle 11
Answer:
my best answer is C) angle 7. But there is not much context so i'm not 100% sure
Step-by-step explanation:
Tea that sells for $2.00 a pound is mixed with a different tea that sells for
$5.00 a pound to produce 40 pounds of a custom blended tea that will
sell for $4.25 a pound. How many pounds of the less expensive tea
should be used in the mixture?
(1) 10
(2) 15
(3) 25
(4) 30
Pls help hellooooo I’ve asked this 5 times and nobody as helped me pls pls pls lsl
Answer:
3 should be the answer to your question
X=-3±2√2
Solve for x
answers are in the photo
goodluck
what are three fractions between 1/8 and 3/4
Answer:
5/32, 3/16, 1/4
Step-by-step explanation:
Make an common denominator: multiply 1/8 by 4/4 to get 4/32
Multiply 3/4 by 8/8 to get 24/32
all possible values: 4/32 through 24/32
5/32
6/32 (Divide by 2 => 3/16 )
8/32 (Divide by 8 to get 1/4)
I need some help please. Given the functions, complete the sections. a) Find the intercepts with the axes. b) Indicate the basic function that you will use to graph it. c) Identify the transformations that your graph will undergo, starting from its basic function. d) Draw the sketch showing the transformations, taking into account all the previous sections. Highlight f(x) with a pen or marker. e) Determine its domain and range.[tex]f(x) = - \frac{1}{4} \sqrt{8 - 4x} + 1[/tex]
a)
The x-intercept can be found as:
[tex]\begin{gathered} f(x)=0 \\ so\colon \\ -\frac{1}{4}\sqrt[]{8-4x}+1=0 \\ -\frac{1}{4}\sqrt[]{8-4x}=-1 \\ \sqrt[]{8-4x}=4 \\ 8-4x=16 \\ 4x=8-16 \\ 4x=-8 \\ x=-\frac{8}{4} \\ x=-2 \end{gathered}[/tex]Therefore, the x-intercept is: (-2,0)
The y-intercept can be found evaluating the function for x = 0, so:
[tex]\begin{gathered} f(0)=-\frac{1}{4}\sqrt[]{8-4(0)}+1 \\ f(0)=1-\frac{\sqrt[]{2}}{2} \\ f(0)\approx0.29 \end{gathered}[/tex]b) The parent function for this is given by:
[tex]g(x)=\sqrt[]{x}[/tex]c)
1st: A reflection over y-axis:
[tex]\begin{gathered} y=g(-x) \\ y=\sqrt[]{-x} \end{gathered}[/tex]2nd: A horizontal compression:
[tex]\begin{gathered} y=g(-4x) \\ y=\sqrt[]{-4x} \end{gathered}[/tex]3rd: A horizontal translation 8 units to the left:
[tex]\begin{gathered} y=g(x+8) \\ y=\sqrt[]{-4x+8}=\sqrt[]{8-4x} \end{gathered}[/tex]4th: A reflection over y-axis:
[tex]\begin{gathered} y=-g(x) \\ y=-\sqrt[]{8-4x} \end{gathered}[/tex]5th: A vertical compression:
[tex]\begin{gathered} y=\frac{1}{4}g(x) \\ y=-\frac{1}{4}\sqrt[]{8-4x} \end{gathered}[/tex]6th: A vertical translation 1 unit up:
[tex]\begin{gathered} y=g(x)+1 \\ y=-\frac{1}{4}\sqrt[]{8-4x}+1 \end{gathered}[/tex]d)
Where the blue graph is the parent function:
[tex]g(x)=\sqrt[]{x}[/tex]And the red graph is the function after the transformations:
[tex]f(x)=-\frac{1}{4}\sqrt[]{8-4x}+1[/tex]e)
The domain and the range are:
[tex]\begin{gathered} D\colon\mleft\lbrace x\in\R\colon x\le2\mright\rbrace \\ R\colon\mleft\lbrace y\in\R\colon y\le1\mright\rbrace \end{gathered}[/tex]Susan is unpacking a full box after moving. She removes a 9 in. x 18 in. x 20 in. computer from the box below. How much volume do the rest of the items in the box take up (in cubic inches)?
The volume the rest of the items in the box take up (in cubic inches) is (x-3240) cu in.
What is volume?
Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m^3, cm^3, in3, etc.Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.Various forms have various volumes.Let the volume of the full box be = x cu in
The volume of the computer box = 9 in. x 18 in. x 20 in. = 3240 cu in
Volume the rest of the items in the box take up (in cubic inches)
= x cu in - 3240 cu in = (x-3240) cu in
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My daughter needs help with her homework I’m confused she’s supposed to fill in the missing digits
Answer:
A is 5
B is 3
C is 2
D is 4
E is 3
F is 5
What is x in the table below.
Green
2
3
5
6
10
Red
6
9
15
18
X
Answer
3.333
30
3
.333
Answer:
(b) 30
Step-by-step explanation:
Given a set of ordered pairs (green, red) = {(2, 6), (3, 9), (5, 15), (6, 18), (10, x)}, you want to know the value of x.
ProportionThe ratio of the red value to the green value is 6/2 = 3 in each case. To keep that ratio, we must have ...
x/10 = 3
x = 30 . . . . . . multiply by 10
What's the circumference of a circle with a radius of 5 inches
Answer:
31.4
Step-by-step explanation:
C=2πr=2·π·5≈31.41593in
The county fair charges $4 for 8 rides and $10 to get
in. If you have $32, write and solve an equation to
find the number of rides (r) you can go on.
it has been determined with 95% confidence that the proportion of on-line students at spc who live in pinellas county is between 0.73 and 0.77. determine the margin of error associated with this confidence interval.
The margin of error associated with the confidence interval is 0.02.
The 95% confidence interval for the population proportion is defined as:
p ± z(0.05 / 2) × √[p ( 1 − p )/ n]
We have,
p − z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.73 ----------- ( 1 )
p + z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.77 ----------- ( 2 )
Adding the above two equations,
p − z(0.05 / 2) × √[ p ( 1 − p )/ n ] + p + z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.73 + 0.77
2p = 0.73 + 0.77
2p = 1.5
p = 0.75
Now, Subtracting the equations ( 1 ) and (2),
We get,
p − z(0.05 / 2) × √[ p ( 1 − p )/ n ] - p - z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.73 - 0.77
−2 × z(0.05 / 2) × √[ p ( 1 − p )/ n ] = -0.44
z( 0.10 / 2) × √[ p ( 1 − p )/ n] = 0.02
The margin of error is defined by the formula:
M E = z(0.05 / 2) × √[ p ( 1 − p )/ n]
Therefore, The margin of error will be:
M E = 0.02
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(12)^1/6
—————
(3)^1/2 (2)^1/3
Answer:
I can't tell if this is division or two separate answers. So, I'll answer both!
Division: 0.222
Answer to (12)^1/6: 2
Answer to (3)^1/2(2)^1/3: 1
b) Solve x^2 + 5x + 6 = 0
Answer: (x+2)(x+3)
Step-by-step explanation:
1) Try to simplify with the line method
List the multiplicative numbers for a and c.
x^2 + 5x + 6 = 0
1x-----------> 3
1x-----------> 2
3 + 2 = 5
Make sure the two numbers multiply-add to b
Afterward, flip the top and bottom numbers.
1x--------------> 2
1x--------------> 3
Put them into an equation.
(x+2)(x+3)
two non-decreasing sequences of nonnegative integers have different first terms. each sequence has the property that each term beginning with the third is the sum of the previous two terms, and the seventh term of each sequence is . what is the smallest possible value of ?
The smallest possible value of the seventh term of the sequence is 104 .
A sequence is an ordered group of items in mathematics where repetitions are permitted and order is important.
Similar to a set, it has members (also called elements, or terms). The size of the series is the amount of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important.Let the first two terms of the first sequence be a and b and the first two of the second sequence be c and d.
Computing the seventh term,
we see that 5a + 8b = 5c + 8d.
Note that this means that a and c must have the same value of |8|.
To minimize, let one of them be 0;
We assume that a= 0.
Thus, the smallest possible value of c is 8; and since the sequences are non-decreasing we get d > 8.
To minimize, let d = 8. Thus, 5c + 8d = 40 + 64 = 104.
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help please!!!!!!!!!!!!
In the estimation, the missing values are 8 and 1 respectively.
How to work out the missing valuesApproximation is the process of using rounded values when presenting numerical data and making rough calculations.
The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up.
Since the number after the digit 8 in 8.41 is 4, we will round down 8.41 to 8
Also, the number after the digit 0 in 0.61 is 6, so we will round up 0.62 to 1
Therefore, the missing values in the estimation are 8 and 1 respectively.
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Use the Distributive
nt Property to find an equivalent
expression:
5(3x-7)
Suppose that 11 inches of wire costs 66 cents.
At the same rate, how much (in cents) will 21 inches of wire cost?
Answer:
8 inches can be purchased for 32 cents.
Does this table show a proportional relationship? If so, what is the constant of proportionality?
A Yes; 1/5
B Yes; 5
C Yes; 10
D The quantities are not proportional.
We can conclude that (A) yes, the table shows the constant of proportionality of 1/5.
What is the constant of proportionality?The ratio connecting two given values in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.So, the constant of proportionality of the given table:
Formula: k = y/x
So, substitute the values in the formula as follows:
8/40 = 1/510/50 = 1/512/60 = 1/514/70 = 1/5So, yes, the table shows the constant of proportionality of 1/5.
Therefore, we can conclude that (A) yes, the table shows the constant of proportionality of 1/5.
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identify the incorrect statement describing the sample sizes and time frames for conducting the various stages of human clinical trials: group of answer choices stage 3: 500-50,000 individuals - usually 4-5 years stage 4: millions of individuals - between 1-2 years stage 1: 5-50 individuals (healthy, young); few weeks to months stage 2: 50-500 individuals (cross section, more cohorts) - months to years
The incorrect statement is 50-500 individuals (cross section, more cohorts) - months to years
The answer provided above has been developed in a clear step by step manner.
Stage 1: 5-50 individuals (healthy, young); few weeks to months is correct considering the hypothesis
Second option is incorrect
Stage 2: 50-500 individuals (cross section, more cohorts) - months to years
Stage 3: 500-50,000 individuals - usually 4-5 years is also correct
Stage 4: millions of individuals - between 1-2 years is also correct
Appropriate sample size generally depends on the specified statistical hypotheses and a few study design parameters. These include the minimal meaningful detectable difference (effect size), estimated measurement variability, desired statistical power, and significance level
Therefore,50-500 individuals (cross section, more cohorts) - months to years can't be used to describe the sample sizes and time frames for conducting the various stages of human clinical trials
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Leah can run 720 yards in 4.5 minutes. How many yards can she run in 2 minutes at the same rate?
A. 350
B. 320
C. 160
D. 110
By the concept of unitary method she can run 320 yards in 2 minutes at the same rate.
What is meant by unitary method?The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach might be helpful for answering questions on ratio and proportion, algebra, and other subjects. "It is a method where we get the value of a single unit from the value of many units and the value of multiple units from the value of a single unit." bra, geometry, etc. Before determining the value of additional or less items, we must first determine the value of one item by dividing it. There are two categories of unitary approaches.
Direct VariationIndirect Variation720 yards = 4.5 minutes
1 minute = 720/4.5
= 160 yards
2 min = 160(2)
= 320 yards
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Solve the equation 6 = -3(s+2)
Answer:
-4 = s
Step-by-step explanation:
6=-3(s+2) multiply -3 into the parenthesis.
6=-3s-6 add 6 to the other side
12=-3s divide by -3 on both sides.
-4=s
Approximate pi plus the square root of forty to the nearest hundredth.
To the nearest hundredth, pi + the square root of forty roughly equals 9.47. The best choice is B.
What does it mean to round a number to a particular place?Rounding a number to a particular value reduces the complexity of the number while increasing readability and accessibility.
When you round to a certain point, the exact digits are maintained on the left side of that point but are rounded or somewhat trimmed from the right.
The limit is set at five.
All right-sided values are made zero if the right-side digit to the digit where we must round off is less than or equal to five; otherwise, it is increased by one and the remaining right-side digits are made zero. If the digit to the right of the decimal point is 5, and there are just zeros or no values after it, we round up (raise by 1 as in 347500 to 34800). (Well there are many detailed rules of rounding)
The following can be used to represent the provided expression, "pi plus the square root of forty to the closest hundredth,"
π + √40
= 3.1416 + 6.3245
= 9.4661 ≈ 9.47
Value is therefore 9.47.
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what unit would you use to measure the length of a parking lot
A yard is a unit of measurement of length equal to 3 feet or approximately 0.914 meter. Hence, to measure the length of a parking lot we use unit yard
What is a Unit ?
A unit, like a building block, is a single, complete portion of something. Before moving on to another unit on geometry in math class, you might complete a unit on algebra. There are also other types of units of measurement, such inches and miles.
Since we know that
A Parking lot is a big area
So we should take a unit that is used to measure bigger area
Thus we use yard for measuring the Parking lot
A yard is a unit of measurement of length equal to 3 feet or approximately 0.914 meter
Hence, to measure the length of a parking lot we use unit yard
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Explain why the statement line LR ≅ line RL and ∠CBA ≅ ∠ABC are both true by the Reflexive Property of Congruence.
The statement line LR ≅ line RL and ∠CBA ≅ ∠ABC are both true by the Reflexive Property of Congruence due to being a reflection of itself
What is reflexive property of congruence?The reflexive property of congruence says that the considered geometric quantity, whether it be angle, line segment, or shape etc, is congruent to itself.
WE have been given that the statement line LR ≅ line RL and ∠CBA ≅ ∠ABC are both true by the Reflexive Property of Congruence.
The reflexive property of congruence says that any geometric figure is congruent to itself.
Any figure being a reflection of itself and that is why they are congruent. For example, the triangle ∠CBA is congruent to ∠ABC.
The statement line LR ≅ line RL and ∠CBA ≅ ∠ABC are both true by the Reflexive Property of Congruence due to being a reflection of itself
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