The information in the word problem indicates that the initial total number of marbles that were given to the three of them at the beginning of the game was 40 marbles
What is a word problem in mathematics?A word problem consists of describing a situation as well as providing the necessary information to a question verbally that is to be solved by by calculations mathematically.
The initial number of marbles Brea had = 10
The number of marbles Brea had at the end = 0
Let A represent the number of marbles given to Abby, let B represent the number of marbles given to Brea and let C represent the number of marbles given to Cleo, we get;
The number of marbles Abby gave Brea and Cleo = B + C
The number of marbles Brea gave Abby and Cleo = (A - (B + C)) + 2·C
B = 10The number of marbles Brea gave Abby and Cleo = All her marbles = 2·B
2·B = 2 × 10 = 20Therefore;
20 = (A - (B + C)) + 2·C = (A - (10 + C)) + 2·C
20 = A - 10 + C
A + C = 20 + 10 = 30
A + B + C = A + 10 + C = A + C + 10 = 30 + 10 = 40
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when engaging in weight control (fitness/fat burning) types of exercise, a person is expected to attain about 60% of their maximum heart rate. for 20-year-olds, this rate is approximately 120 bpm. a simple random sample of 100 20-year-olds was taken, and the sample mean was found to be 107 bpm with a standard deviation of 45 bpm. researchers wonder if this is evidence to conclude that the expected level is actually lower than 120 bpm. to determine this, we test the following hypotheses suppose the mean and standard deviation obtained were based on a sample of size 25 rather than 100. the p-value would be
There is sufficient data to prove that the heart rate was less than 120 beats per minute (P-value = 0.002).
For the population mean weight control heart rate of 20-year-olds, the 95% confidence interval is (98.07, 115.93).
Step-by-step explanation:
This is a test of the population mean's theory.
The assertion is that a heart rate of less than 120 bpm exists.
The alternative and null hypothesis are then:
h0 : μ = 120
ha : μ < 120
The level of significance is 0.05.
The sample has a n=100 size.
M=107 is the sample mean.
Due to the unknown population standard deviation, we estimate it using the sample standard deviation, which has a value of s=45.
Using the following formula, the estimated standard error of the mean is calculated:
Sm = [tex]\frac{s}{\sqrt{n} }[/tex]= [tex]\frac{45}{\sqrt{100} }[/tex] = 4.5
The t-statistic can then be calculated as follows:
T = [tex]\frac{m-μ}{\frac{s}{\sqrt{n} } }[/tex] = 107-120/4.5 = -13/4.5 -2.88
The t-statistic can then be calculated as follows:
df= n-1 = 100-1 = 99
These sample size's degrees of freedom are:
Given that this test has 99 degrees of freedom, a left-tailed design, and a t value of -2.889, the P-value is determined as follows (using a t-table)
p-value = p(t<-2.88)= 0.002
The effect is significant because the P-value (0.002) is less than the 0.05 level of significance.
The naive theory is disproved.
There is sufficient proof to back up the assertion that the heart rate was less than 120 bpm.
A 95% confidence interval for the mean must be calculated.
Since the population standard deviation is unknown, we must infer it from the sample standard deviation in order to get the critical number using a t-students distribution.
M=107 is the sample mean.
N=100 is the sample size.
When σ is unknown, an estimation of σM is made by dividing s by the square root of N:
Sm =[tex]\frac{s}{\sqrt{N} }[/tex] =[tex]\frac{45}{\sqrt{100} }[/tex] =4.5
The t-value for a 95% confidence interval is t=1.984.
The margin of error (MOE) can be calculated as:
MOE = t*Sm = 1.984 * 4.5 = 8.92
Then, the lower and upper bounds of the confidence interval are:
LL = M - t*Sm = 107- 8.92 = 98.07
UL = M +t *Sm = 107 + 8.92 = 115.93
The 95% confidence interval for the population mean weight control heart rate of 20-year-olds is (98.07, 115.93).
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Write the quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form.
I know how to write it in standard form- f(x)=2x^2+4x-6
But I don’t know how to write it in intercept form.
Please explain.
The quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).
Given:
f(x) = 2(x+1)^2 - 8
= 2(x^2+1+2x) - 8
= 2x^2 + 2 +4x - 8
= 2x^2+4x-6(standard form)
Intercept form:
= 2x^2+4x-6
= (x-1)(x+3)
x-1 = 0
x = 1
x+3 = 0
x = -3
(1,0) and(-3,0).
Therefore the quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).
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please help me on this!
Answer:
Step-by-step explanation:
Ok:
First Problem with coin!
1. A coin has 2 sides and one of them is going to land up or down which means it has a chance of 1 out of 2.
1 out of 2=
1/2= 50%
Second Problem with spinner
2. There are 12 spaces on the spinner and three of those spaces are blue.
SO: 3 out of 12=
3/12=
1/4=
25%
Answers: 50% and 25%
IN FRACTION FORM: 1/2 and 1/4
find all the whole values of a for which the soultion of the equation ax=6 is a whole number
The whole values of a for which the solution of the equation ax = 6 is a = {1, 2, 3, 6}
The given equation is
ax = 6
Divide both side of the equation by a
ax / a = 6/a
Then the equation will be
x = 6/a
If the solution of the system should be a whole number, then the value of a should be a factor of the numerator 6.
If a is the factor of 6, then the only the result will be a whole number without any numerator
Then the factors of 6 are 1, 2, 3, 6
Then the whole values of a = {1, 2, 3, 6}
Hence, the whole values of a for which the solution of the equation ax = 6 is a = {1, 2, 3, 6}
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some people claim they can get relief from migraine headache pain by drinking a large glass of ice water resources plan to enlist several people who suffer from migraines and i test
The correct response variable is the amount of pain relief.
Given that,
A tall glass of ice water, according to some, can help migraine sufferers find relief. Multiple migraine sufferers will be recruited by researchers to participate in a test. The individual will either take a placebo pill or a common painkiller when they get a migraine. Additionally, only half of each group will take the pill with water; the other half will sip on a small amount of water. The quantity of pain relief is then reported by participants.
To find : What is the response variable in this experiment.
Explanation :
Response variable or study variable, in general called as dependent variable is the variable of main focus in study. We want to study the changes in explanatory or independent variables are associated with response variable. Sometimes we want to measure the effect of predictors i.e explanatory variables on response variable.
For example in hand, we want to determine whether the drinking ice water is associated with amount of pain relief. Hence in this study, response variable is the amount of pain relief.
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What are the coordinates of the image of vertex P?
Answer:
P'(-16, 0)
Step-by-step explanation:
You want the coordinates of the image of P(-4, 0) when the figure is dilated by a factor of 4 about the origin.
DilationDilation about the origin multiplies each coordinate by the dilation factor:
P' = 4P
P' = 4(-4, 0) = (-16, 0)
The coordinate of the image point are (-16, 0).
when the point (-2, 6) is reflected across the y-axis it will be located at where
The point (-2, 6) is reflected across the y-axis then the new coordinates of the point are (2, 6).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
We know when a point (x, y) is reflected along the y-axis (x, y) becomes
(- x, y).
Given, A point (-2, 6) is reflected across the y-axis.
∴The new coordinates of the point are (2, 6).
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please help !!!!! asapppp
Answer:
C
Step-by-step explanation:
there are 1 x values that have the 2 different y value
The old energy level is 250. A bar is added to the bag. The new energy level is 400. Complete the equation.
The equation is, 250+x =400
From the question, we have
The old energy level is 250.
Let the bar is added to the bag = x.
The new energy level is 400.
The equation is, 250+x =400
Addition:
The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.
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Got a question in connexus 8th grade advanced Math XL
The words that describe the pattern that can be used to complete the table is that the number of lines is double the number of figures, which indicates that the correct option is option A
A. The total number of lines y is two times the figure number x
The equation that represents the relationship is; y = 2·xWhat is an equation?
An equation is a mathematical statement that connects two expression with an equals sign.
The number of lines in one figure = 2 linesThe number of lines in two figures = 4 linesThe number of lines in 3 figures = 6 linesTherefore, the number of lines in n figures = 2·n linesThe pattern that can be used to complete the table is therefore;
The number of lines, y, is twice the number of figures, x
The relationship expressed mathematically as an equation is presented as follows;
y = 2·x
The completed table is presented as follows;
Figure Number, x [tex]{}[/tex] Total Lines, y [tex]{}[/tex] Ordered pair
1 [tex]{}[/tex] 2 (1, 2)
2 [tex]{}[/tex] 4 (2, 4)
3 [tex]{}[/tex] 6 (3, 6)
4 [tex]{}[/tex] 8 (4, 8)
5 [tex]{}[/tex] 10 (10, 5)
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Triangle PQR with vertices P(-13,-3) Q(-7,3) R(-6,-2) 270 degrees counterclockwise rotation about C(-5,-4)
Check the picture below.
Makayla earned $1,155 in interest from her simple interest account over
the last 5 years. The account pays 1.25% interest annually. How much did
Makayla originally deposit in his account?
Answer:2
Step-by-step explanation:
1. Write a system of inequalities (you do not need to solve): You need at least 3 pounds of fruit to make muffins. Blueberries cost $4 per pound. Strawberries cost $3 dollars a pound. You can spend at most $21.
the slope between the points (-4,4) (-15,2)
To calculate the distance between two points, we have to:
[tex]\large\displaystyle\text{$\begin{gathered}\sf The \ points\ are \left \{ {{A=(x_1,y_1)} \atop {B=(x_2,y_2)}} -\to\boldsymbol{\sf{m=\frac{\Delta y}{\Delta x }\iff \ m=\frac{y_2-y_1}{x_2-x_1} }} \right. \end{gathered}$}[/tex]
We have that the points to calculate the slope are: (x₁ = -4, y₁ = 4) and (x₂ = -15, y₂ = 2)
Add the data in the formula:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{y_2-y_1}{x_2-x_1} } \end{gathered}$}} \\ \\ \boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{2-4}{-5-(-4) } } \end{gathered}$}} \\ \\ \boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2}{-11} } \end{gathered}$} }}[/tex]
La pendiente entre los puntos (-4,4) (-15,2) es -2/11.I more questions i have a lot coming
Answer:
Step-by-step explanation:
4x-c=k
solve for x
use the reverse order for the usual order of operations, to solve for x
first use addition
4x = k+c
then use division
x = (k+c) / 4
so answer B) looks good
PEASE HELP ME AAAAA
^.^♡
You have a budget of 300 to order shirts for math club. The equation 10x +12y=300 models the total cost, where x is the number of short-sleeved shirts and y is the number of Ling-sleeved shirts.
/////
a.) Interpret the terms and coefficients in the equation.
____(Write here)_____
///
Graph the equation - on photo>
///
b.) Interpret the intercepts.
___(write here)___
///
c.) Find three possible solutions in the context of the problem.
a) The terms are: 10x, 12y,300
The Coefficients are: 10,12
b) x intercept is (30,0). y intercept is (0,25)
c) The three possible solutions:
(1,24), (8,18) , (6,20)
what are terms and coefficients?
Term could be a single number (positive or negative), a single variable (a letter), or a combination of multiple variables multiplied but never added or removed. Variables with numbers in front of them can be found in some terms. A coefficient is the number that appears in front of a phrase.
10x +12y=300
Terms: 10x, 12y,300
Coefficients: 10,12
Refer to the attachment for graph:
b) The locations on a Cartesian coordinate system known as intercepts are where the graph of an equation or function crosses the x- and y-axes.
From the graph, x intercept is (30,0). y intercept is (0,25)
c) solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
10x +12y=300
Find y when x=1:
10(1)+12y=300
10+12y=300
12y=300-10=290
y= 24.2 ≈ 24
Similarly, the three possible solutions:
(1,24), (8,18) , (6,20)
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hello! i really need help
The sales tax is $1.2 and the total cost of the item is $21.2 .
In the question,
it is given that ,
the selling price of the item is $20.
the rate of sales tax is = 6^ ,
so the sales tax can be calculated using the formula
sales tax = 6% of selling price
So , sales tax = 6% of 20
= 0.06 * 20
= 1.2
so , the sales tax is $1.2
the total cost of the item will be = selling price + sales tax
= 20 + 1.2
= 21.2
Therefore , The sales tax is $1.2 and the total cost of the item is $21.2 .
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Construct a square with vertex A inscribed in the given circle
Answer:
see attached
Step-by-step explanation:
You want to construct an inscribed square in circle C with vertex A.
StepsReference the attached figure.
With the compass set to a radius greater than AC, draw arc BE centered at A.With the same compass setting, draw arc GH centered at F, which is the second intersection of line AC with circle C.Identify the points where the arcs intersect as I and J. Draw line IJ.Identify the points where line IJ intersects circle C as K and L.The desired inscribed square is AKFL.
What is the value of y in the equation 4+y=-3
Answer:
y=-7
Step-by-step explanation:
just simplify it
4+y=-3
y=-3-4
y=-7
What is a sampling proportion?
Answer:
it describes the proportion of individuals in a sample with a certain characteristic or trait
Step-by-step explanation:
to find sampling proportion, u have to divide the number of people or items who have the characteristic of interest by the total number of people/items in the sample.
It describes the percentage of people in a sample who possess a particular quality or attribute.
What is a sampling proportion?
The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.
Formula to calculate sampling proportion
p′ = x / n
where,
x: the number of successes
n: the sample size
p′: sample proportion
Hence, it describes the percentage of people in a sample who possess a particular quality or attribute.
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Which of the functions is represented by the graph
O f(x)=2x²+3
O f(x) = -x² + 3
O f(x) =1/2x² + 3
O f(x) = -1/2x +3
Pls help
Answer:
[tex]f(x)=-2x^2+3[/tex]
Step-by-step explanation:
The vertex is at [tex](0,3)[/tex], so the equation is of the form [tex]f(x)=ax^2+3[/tex].
Using the point [tex](1,1)[/tex] to solve for [tex]a[/tex],
[tex]1=a+3 \implies a=-2 \\ \\ \therefore f(x)=-2x^2+3[/tex]
Can anybody help me with this?
On 6th day the Blake and Nicole will be on same page
Consider the case of Blake
The initial page number = 40
Number of pages per day = 10
Consider the B is the page number and t is the number day
Then the function will be
B = 40 + 10t
Consider the case of Nicole
The initial page number = 10
Number of pages per day = 15
Consider the N is the page number and t is the number day
Then the function will be
N = 10 + 15t
Draw the graph using the functions
Hence, on 6th day the Blake and Nicole will be on same page
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A store manager buys 8 T-Shirts and 5 hats for $220. The next day, the manager buys 5 T-shirts and 1 hat for $112.
Part A
Select the system of equations that models the situation.
A. 8t + 5h = 220
t + 5h = 112
B. 13(t – h) = 220
6(t – h) = 112
C. 8t + 5h = 220
5t + h = 112
Part B
How much does each T-shirt and each hat cost?
T-shirt : $
Hat : $
Answer:
Part A: C
Part B: T shirt = $20, hat = $12
Step-by-step explanation:
Part A:
He buy 8 T-Shirts and 5 hats for $220.
He buy another buys 5 T-shirts and 1 hat for $112.
assuming t = tshirt, h = hat, C is the correct answer
Part B:
8t + 5h = 220
5t + h = 112
1. Use second equation to represent h in term of t
h = 112 -5t
2. Replace h in first equation with h from 1.
8t + 5(112 -5t) = 220
8t + 560 - 25t = 220
-17t + 560 = 220
-17t = 220 - 560
-17t = -340
t = -340/-17 = 20
3. Replace t in equation from 1. with t from 2.
h = 112 -5(20) = 112 - 100 = 12
How would I get the slope
answer this i dare you If a seventh grader gets closer to the record-setting jump, then the seventh graders earn 100 points. If not, the eighth graders earn 100 points. Which grade should be awarded 100 points?
Answer: 7th Graders
Explanation:
Several people have gotten this question and 7th graders are the right choice
Answer:7th grade should be awarded !
Step-by-step explanation:
A pupil wrote:
for all numbers j and k,
(j+k)² = j² + k²
Expand and simplify (j+k)² to show that the pupil is wrong.
Answer:
see explanation
Step-by-step explanation:
(j + k)²
= (j + k)(j + k)
each term in the second factor is multiplied by each term in the first factor , that is
j(j + k) + k(j + k) ← distribute parenthesis
= j² + jk + jk + k² ← collect like terms
= j² + 2jk + k²
Rectangle WXYZ is shown. W Z Y If WY=12m +7 and XZ = 16m-43, what is the value of m? Enter the answer in the box in decimal form. Use "." for the decimal point. X m=
The value of the variable m in the rectangle is given as follows:
m = 12.5.
How to obtain the measure of variable m?The segments from the rectangle, and their lengths, are given as follows:
WY = 12m + 7.XZ = 16m - 43.They are opposite vertices of the rectangle, as they do not have any common vertex.
Since they are opposite vertex, it doesn't matter if these segments are bases, heights or diagonals, they will have the same length.
Thus the numeric value of variable m is obtained as follows:
WY = XZ
(as they have the same length).
Replacing the measures of each of these segments:
12m + 7 = 16m - 43
12m - 16m = -43 -7
-4m = -50
4m = 50 (multiplication by -1).
m = 50/4
m = 12.5.
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Assume that the diameter d of a circle is a differentiable function of t, and let C be the circumference of the circle. Find an equation that relates dC/dt and dd/dt.
A. C = πd
B. dC/dt = πd
C. dC/dt = π (dd/dt)
D. dC/dt = πd (dd/dt)
Option C is correct which is dC/dt = π (dd/dt).
According to the question,
We know that the diameter of the circle is half the radius of the circle.
d = r/2
By transferring r to the left-hand side and d to the right-hand side
r = d/2
We also know that circumference of the circle is
C=2πr
C=2πd/2
C=πd
Now we will differentiate on both the side with respect to t and we will get,
dC/dt = π (dd/dt)
Differentiation is a technique for tracking down the subordinate of a capability. Differentiation is a process, where we find the momentary rate of change in capability in light of one of its variables. We usually differentiate with respect to time which is represented as ds/dt.
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Find the multiplier of 0.5%
The multiplier of 0.5% is 0.005
How determine the multiplier of 0.5%?
A percentage multiplier is a number that is used to calculate a percentage of an amount
In order to determine 0.5% of a number we can multiply the number by a multiplier:
0.5% = 0.5/100 = 0.005
Therefore, 0.005 is the multiplier
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Simplify.
1+3²⋅2−5
the answer is either -48, 14, 15, or 27.