Answer:
Use systems of equations to solve.
Let x represent the cost per pound of the espresso coffee beans and
y represent the cost per pound of the vanilla coffee beans.
6x + 5y = 77.50
20x + 13y = 234.50, both of these are given.
Rewrite these equations so you can eliminate one of the variables;
60x + 50y = 775, Multiply both sides of the equation by 10
60x + 39y = 703.5, Multiply both sides of the equation by 3
Now Subtract equation 2 from equation 1,
11y = 71.5
y = 6.5
Solve for x,
6x + 5(6.50)= 77.50
x = 7.50
Therefore, the cost per pound of the espresso coffee beans is $7.50, and
the cost per pound of the vanilla coffee beans is $6.50.
Can someone please help:(
Thank you all
There were 172 children and 165 adults admitted to the amusement park.
Given that the admission fee for children is $1.50, so the total amount collected from children is 1.5c.
Similarly, the admission fee for adults is $4, so the total amount collected from adults is 4a.
We are also given that the total number of people admitted to the park is 337, so we can write the following equation based on the number of people:
c + a = 337
The total admission fees collected is $918.
1.5c + 4a = 918
Now we have a system of two equations.
From the first equation, we can express 'c' in terms of 'a':
c = 337 - a
Substituting this value of 'c' into the second equation:
1.5(337 - a) + 4a = 918
505.5 - 1.5a + 4a = 918
2.5a = 918 - 505.5
2.5a = 412.5
a = 412.5 / 2.5
a = 165
Substituting the value of 'a' back into the first equation:
c + 165 = 337
c = 337 - 165
c = 172
Therefore, there were 172 children and 165 adults admitted to the amusement park.
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In a club there are 8 women and 5 men. A committee of 4 women and 3 men is to be chosen. How many different ways are there to select the committee?
The number of ways of selecting a committee of 4 women and 3 men from 8 women and 5 men is 700 ways
How do i determine the number of ways of selecting the committee?First, we shall obtain the number of ways to choosing a committee of 4 women from 8 women. This is given below:
Number of items (n) = 8Number of items selected (r) = 4Selecting 4 women from 8 women [C(8, 4)] = ?C(n, r) = n! / [r!(n - r)!]
C(8, 4) = 8! / [4!(8 - 4)!]
C(8, 4) = 70 ways
Next, we shall obtain the number of ways to choosing a committee of 3 men from 5 men. This is given below:
Number of items (n) = 5Number of items selected (r) = 3Selecting 3 men from 5 men [C(5, 3)] = ?C(n, r) = n! / [r!(n - r)!]
C(5, 3) = 5! / [3!(5 - 3)!]
C(5, 3) = 10 ways
Finally, we shall determine the Total ways of selecting the committee. Details below:
Selecting 4 women from 8 women [C(8, 4)] = 70 waysSelecting 3 men from 5 men [C(5, 3)] = 10 waysTotal ways of selecting =?Total ways of selecting = [C(8, 4)] × C(5, 3)]
Total ways of selecting = 70 × 10
Total ways of selecting = 700 ways
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the sum of 9 and x is at least -23. Translate the sentence into an inequality
Answer:
9 + x ≥ -23
Step-by-step explanation:
'At least' here means the lowest possibility of the sum 9 + x can equal -23, which means 9 + x can also be greater than -23. So the sum is either equal to -23 or greater than -23.
Please I need this answer
Answer:
FE = 12
DE = 20
Step-by-step explanation:
Part A
We can solve for FE by equating the ratios of the triangles' sides. Remember we can only do this because the triangles are similar, so the scale factor between the side lengths is the same.
[tex]HE : GH = FE : DF[/tex]
↓ plugging in the given values
[tex]9 : 12 = FE : 16[/tex]
↓ representing as fractions
[tex]\dfrac{9}{12} = \dfrac{FE}{16}[/tex]
↓ multiplying both sides by 16
[tex]\boxed{FE = 12}[/tex]
Part B
We can solve for DE using the same technique.
[tex]GE : GH = DE : DF[/tex]
↓ plugging in the given values
[tex]15 : 12 = DE : 16[/tex]
↓ representing as fractions
[tex]\dfrac{15}{12}= \dfrac{DE}{16}[/tex]
↓ multiplying both sides by 16
[tex]\boxed{DE = 20}[/tex]
A scientist has two solutions what she has labeled solution a and solution b each contains salt she knows that solution a is 60% salt and solution b is 85% salt she wants to obtain 70 ounces of a mixture that is 80% salt how many ounces of each solution should she use
Solving a system of equations we can see that:
She needs to use 56 oz of the 85% solution.She needs to use 14 oz of the 60% solution.How many ounces of each solution should she use?We can use the variables:
x = mass of the 60% solution.
y = mass of the 85% solution.
We can write a system of equations.
x + y = 70
x*0.6 + y*0.85 = 70*0.8
We can isolate x on the first equation to get:
x = 70 - y
Replace that in the other one:
(70 - y)*0.6 + y*0.85 = 70*0.8
Now we can solve this for y.
y*0.25 = 70*0.8 - 70*0.6
y = 14/0.25 = 56
Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.
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Calculate the average Budget across the four quarters.
Next year, it is estimated that there will be an average
budget of £6,032 per quarter. How much more is this, as a
percentage?
6,500
5,500
4,500
3,500
2,500
1.500
Budget and Project Costs
(£GBP)
5,623
1,670
Quarter 1
5,892
1,903
Quarter 2
Costs
6,382
2,104
Quarter 3
Budget
Q Search
5,325
1,790
Quarter 4
a
Please select the correct answer from the options
shown.
a. 2.9%
b. 3.1%
c. 3.7%
d. 3.9%
Answer:
d
Step-by-step explanation:
To calculate the average budget across the four quarters, we need to add the budget for each quarter and divide by 4:
Average budget = (5623 + 5892 + 6382 + 5325) / 4 = 5805.5
Next year's estimated budget is £6,032 per quarter.
To calculate the percentage difference, we can use the following formula:
Percentage difference = (new value - old value) / old value x 100%
Percentage difference = (6032 - 5805.5) / 5805.5 x 100% = 3.9%
Therefore, the answer is (d) 3.9%.
Thianga buys a car for $75 000. The value of the car depreciates at 15% per year. After 1 year the car is worth 85% of its original value.
How many years will the car be worth less than $15000? without using log
Answer: 6 years
Step-by-step explanation:
75,000*15% = 11,250
11,250*6 = 67,500
75,000-67,500 = 7500
7500 is worth less than 15,000
5 years would have been 18,750; more than 15,000
Evaluate the expression you got in part d for b = 8
It should be noted that when b = 8, the expression b/2 - 3 evaluates to 1.
How to calculate the expressionIn order to evaluate the expression b/2 - 3 when b = 8, we substitute the value of b into the expression and perform the calculations.
Given that b = 8, we have:
8/2 - 3
Now we simplify the expression:
8/2 is equal to 4, so we have:
4 - 3
Finally, subtracting 3 from 4 gives us the result:
4 - 3 = 1
Therefore, when b = 8, the expression b/2 - 3 evaluates to 1.
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b/2-3 Evaluate the expression you got in part d for b = 8
Question A survey asked 10 boys and 10 girls how many text messages they sent the previous day. The number of texts are given in the line plots. Select from the drop-down menus to complete each statement. The data set with the greater range is Choose... . The median Choose... .
The data set with the greater range is greater for girls. The median is greater for girls.
The range of a dataset is the difference between the maximum and minimum values in the set.
The median is the middle value in a sorted dataset, or the average of the two middle values if the set has an even number of elements.
To determine which dataset has a greater range, you need to compare the difference between the highest and lowest values of the two datasets.
To determine which dataset has a larger median, you need to sort the datasets and find the middle value(s).
The range for boys is 60 as for girls the range is 80. The median for boys is 90 and for girl 110.
Hence, the data set with the greater range is greater for girls. The median is greater for girls.
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Is the relation a function?
Yes or No
!PLEASE HELP!
Answer:
Is the relation a function?
no
Step-by-step explanation:
please make brainlist
Triangle ABC, with vertices A(-8,-7), B(-4,-8), and C(-5,-5),
What is the area, in square units, of triangle ABC?
The area of triangle ABC is given as follows:
A = 5.5 square units.
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The base AB has the length given as follows:
[tex]AB = \sqrt{(-4 - (-8))^2 + (-7 - (-8))^2}[/tex]
b = 4.12.
The midpoint of the base AB is given by the mean of the coordinates, hence:
M = (-6, -7.5).
The height is given by the distance MC, as follows:
[tex]h = \sqrt{(-6 - (-5))^2 + (-7.5 - (-5))^2}[/tex]
h = 2.69.
Hence the area of the triangle is given as follows:
A = 0.5 x 4.12 x 2.69
A = 5.5 square units.
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Find the curvature of the curve
Note that the curvature of the curve defined by the function y = 3x² - 2x +4 at point x = 2 is approximately 0.0002.
How did we arrive at this ?To find the curvature of the curve defined by the function, we need to first find the second derivative of the function.
y = 3x² - 2x + 4
Taking the first derivative of y with respect to x
y' = 6x - 2
Taking the second derivative of y with respect to x:
y'' = 6
So the second derivative of y is a constant 6.
To find the curvature of the curve at point x = 2, we need to evaluate the following formula:
k = |y''| / [1 + (y')²][tex]^{(3/2)}[/tex]
Substituting x = 2 and y'' = 6, we get:
k = |6| / [1 + (6x2 - 2)²][tex]^{(3/2)}[/tex]
= 6 / [1 + (22)²][tex]^{(3/2)}[/tex]
= 6 / [1 + 484][tex]^{(3/2)}[/tex]
= 6 / 485[tex]^{(3/2)}[/tex]
k ≈ 0.0002
Hence, the curvature of the curve defined by the function y = 3x² - 2x + 4 at point x = 2 is approximately 0.0002.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Find the curvature of the curve defined by the function
y=3x^2 -2x + 4
at point x =2
PLS HELP Polygon ABCD with vertices at A(1, −2), B(3, −2), C(3, −4), and D(1, −4) is dilated to create polygon A′B′C′D′ with vertices at A′(4, −8), B′(12, −8), C′(12, −16), and D′(4, −16). Determine the scale factor used to create the image.
one fourth
one half
2
4
The scale factor used to create the image is given as follows:
4.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
In the context of this problem, we have that each vertex of A'B'C'D' is obtained with the multiplication of each of the coordinates of ABCD by four.
For example, we have that vertex A has the coordinates A(1, -2), while the equivalent vertex A' has the coordinates of A'(4, -8).
Hence the scale factor used to create the image is given as follows:
4.
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Michelle orders 200 T-shirts to sell at the school carnival. She pays $6.50 per shirt, plus 5% of the total order for shipping. How much does she pay in all?
A $6.83
B $65.00
C $1,235.00
D $1,365.00
Michelle pays $1365 in total.
Option D is the correct answer.
We have,
To calculate the total amount Michelle pays for the T-shirts, we need to consider the cost per shirt and the shipping fee.
The cost per shirt is $6.50, and she ordered 200 shirts, so the cost of the shirts alone is:
= $6.50 x 200
= $1300
The shipping fee is 5% of the total order, which is:
= 5% x $1300
= $65
To find the total amount Michelle pays, we add the cost of the shirts and the shipping fee:
= $1300 + $65 = $1365
Therefore,
Michelle pays $1365 in total.
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Acme toy company prints baseball cards. The company claims that 30% of the cards are
rookies, 60% veterans but not All-Stars, and 10% are veteran All-Stars. Suppose a random
sample of 100 cards has 50 rookies, 45 veteran, and 5 All starts. Is this consistent with
Acme’s claim? Use a 0.05 level of significance to perform a complete hypothesis test. Show
all work.
1. Calculate the Expected values for opening a sample of 100 cards:
2. State the null and alternative hypotheses.
3. Calculate the degrees of freedom.
4. Complete your hypothesis test using the procedures covered in the lecture for
Chapter 11. What are the results?
5. State your conclusions
6. Supposed you got a larger sample, and performed another hypothesis test. What
would you expect to happen, based on your findings?
7. Now, we will think like a sociologist. We are interested in determining whether
there is a relationship (i.e. independent or dependent variables) between gender
and getting in trouble at school. Below is the table documenting the frequency
counts of boys and girls and their respective behavior issues (or lack thereof):
Got in
Trouble
Did Not
Get in
Trouble
Total
Boys 46 71 117
Girls 37 83 120
Total 83 154 237
Show your work here, and come up with a conclusion about these variables using the
methods discussed
Answer:
1 calculate the Expected values for opening a sample of 100 cards
please help! thank uu ~ :)
Help please will Mark brainliest
Answer: B =[tex]x^{\frac{4}{5} }[/tex]
Step-by-step explanation:
Rules needed:
When you have a root, you can write it in exponented form. It becomes a fraction.
EX.
[tex]\sqrt[5]{x} =x^{\frac{1}{5} }[/tex]
When you have a number that is multiplied to another number both have exponents and same bases, you can combine the two by adding the exponents
EX.
[tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } = x^{\frac{2}{5} }[/tex]
Your problem:
[tex]\sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}[/tex] >convert to exponent form
=[tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} }[/tex] >add all exponents [tex](\frac{1}{5} +\frac{1}{5} +\frac{1}{5}+\frac{1}{5})[/tex]
=[tex]x^{\frac{4}{5} }[/tex]
B
Which function equation is represented by the graph?
f(x)=40(2.5)x
f(x)=40(1.5)x
f(x)=40(3.25)x
f(x)=40(2.25)x
Answer:
f(x)=40(2.25)^x
Step-by-step explanation:
You want the equation of the exponential function that goes through points (0, 40) and (1, 90).
Exponential functionThe exponential function can be written ...
f(x) = a·b^x
ParametersWhen x = 0, this is ...
f(0) = a·b^0 = a·1 = a
Using the given point, we have a = 40.
When x = 1, this is ...
f(1) = 40·b^1 = 40b
Using the given point, we have ...
90 = 40b
b = 90/40 = 2.25
The function equation is ...
f(x) = 40(2.25^x)
<95141404393>
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
subsidiaries hi sus
Step-by-step explanation:
scientific 2 is the answer
what is x, I really need help
hello
the answer to the question is:
Tan (x) = 6.7/4.9 = 1.3673 ----> x = 53.81° or 54°
The values in the table represent a linear relationship between x and y.
x -8.5 -6.5 -2.5 -1
y -92 -72 -32 -17
What is the rate of change of y with respect to x?
The rate of change of y with respect to x for the given linear relationship is 10.
To determine the rate of change of y with respect to x, we can calculate the slope of the linear relationship between x and y using the formula:
slope = (change in y) / (change in x)
Given the values in the table:
x: -8.5, -6.5, -2.5, -1
y: -92, -72, -32, -17
We can calculate the change in y and change in x between any two points.
For example, between the first two points (-8.5, -92) and (-6.5, -72), the change in y is:
change in y = -72 - (-92) = -72 + 92 = 20
And the change in x is
change in x = -6.5 - (-8.5) = -6.5 + 8.5 = 2
Using the formula for slope:
slope = (change in y) / (change in x) = 20 / 2 = 10.
Therefore, the rate of change of y with respect to x is 10.
This means that for every unit increase in x, y increases by 10 units.
We can perform the same calculations for the other points in the table and observe that the rate of change of y with respect to x remains constant at 10.
Hence, the rate of change of y with respect to x for the given linear relationship is 10.
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Given P(G∩N)=0.24, P(G)=0.37, and P(N)=0.41. Find P(G|N).
The probability P(G|N) value is 0.585 when P(G∩N)=0.24, P(G)=0.37, and P(N)=0.41.
To find P(G|N), which represents the probability of event G given event N, we can use the formula:
P(G|N) = P(G∩N) / P(N)
Given that P(G∩N) = 0.24 and P(N) = 0.41
we can substitute these values into the formula:
P(G|N) = 0.24 / 0.41
Calculating the division:
P(G|N) = 0.585
Therefore, the value of P(G|N) is 0.585.
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QUESTION 23 - 1 POINT
Solve: 3|x + 1| ≥-6. Write your solution in interval notation.
(If there is no solution, enter your answer as Ø.)
Sure. Here are the steps on how to solve the equation 3|x + 1| ≥-6:
Divide both sides of the equation by 3.
Simplify both sides of the equation.
Isolate x on the left-hand side of the equation.
Test each solution in the original equation to make sure it makes the equation true.
Write the solution in interval notation.
Here are the detailed steps:
Divide both sides of the equation by 3:
3|x + 1| ≥-6
|x + 1| ≥ -2
Simplify both sides of the equation:
|x + 1| ≥ -2
x + 1 ≥ -2 or x + 1 ≤ -2
Isolate x on the left-hand side of the equation:
x + 1 ≥ -2
x ≥ -2 - 1
x ≥ -3
x + 1 ≤ -2
x ≤ -2 - 1
x ≤ -3
Test each solution in the original equation to make sure it makes the equation true.
Test x = -3 in the original equation:
3|-3 + 1| ≥-6
3|-2| ≥-6
3(2) ≥-6
6 ≥-6
True
Test x = -4 in the original equation:
literally struggling so hard
Answer: I think question two is Adjacent angles and complimentary angles.
Step-by-step explanation: Complementary angles are two acute angles that add to form a right angle.
Adjacent angles are two angles that share a common side.
landon invested 110 in an account with an interest rate of 4.1 how much would be there after 5 years
As it only told interest i asume its simple interest for compound interest the answer would be different
An increase from $27 to $35.10 what percent of increase?
Answer:
30% increase
Step-by-step explanation:
percentage increase is calculated as
[tex]\frac{increase}{original}[/tex] × 100%
increase = $35.10 - $27 = $8.10 , then
percentage increase = [tex]\frac{8.10}{27}[/tex] × 100% = 0.3 × 100% = 30%
Answer:
Step-by-step explanation:
step 1: 35.10-27 =8.1
step 2: 8.1/27 x 100 = 30%
so therefore = 30% increase
Which sign makes the statement true?
67.18% ?
7
22
64
V
||
(Please NEED THIS AASP!)
The required sign that makes the statement true is "||".
The given options are 7, 22, 64, and V.
To express a percentage in mathematical notation, we divide the number by 100. In this case, 67.18% can be written as 0.6718.
Using the "||" symbol, we can write the equation as: 0.6718 || 7 = 22.
This equation represents the statement "0.6718 is to 7 as 22 is to 100." The vertical bar "||" signifies the ratio or proportion between the numbers. The double vertical bars "||" typically represent the symbol for "is equivalent to" or "is parallel to" in various contexts.
Therefore, the sign "||" makes the statement true.
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Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.
The coordinates in the solution to the systems of inequalities graphically is (-5, 1)
Solving the systems of inequalities graphicallyFrom the question, we have the following parameters that can be used in our computation:
y < 1/2x + 5
y ≤ -3x - 2
Next, we plot the graph of the system of the inequalities
See attachment for the graph
From the graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities graphically is (-5, 1)
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Answer:
(-5, -5)
Step-by-step explanation:
Given system of linear inequalities:
[tex]\begin{cases}y < \dfrac{1}{2}x+5\\\\y\leq-3x-2\end{case}[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.To graph linear inequalities, treat them as equations (swap the inequality sign for an "equals" sign). Plug in two values of x to find two points on the line to help draw the lines.
Graphing the line y < (1/2)x + 5Substitute x = 0 and x = 6 into the equation of the inequality to find two points on the line.
[tex]\begin{aligned}x=0 \implies y&=\dfrac{1}{2}(0)+5\\y&=5\end{aligned}[/tex] [tex]\begin{aligned}x=6 \implies y&=\dfrac{1}{2}(6)+5\\y&=8\end{aligned}[/tex]
Plots points (0, 5) and (6, 8).
As the inequality sign is <, draw a dashed line through the plotted points and shade below the line.
Graphing the line y ≤ -3x - 2Substitute x = 0 and x = 2 into the equation of the inequality to find two points on the line.
[tex]\begin{aligned}x=0 \implies y&=-3(0)-2\\y&=-2\end{aligned}[/tex] [tex]\begin{aligned}x=2 \implies y&=-3(2)-2\\y&=-8\end{aligned}[/tex]
Plots points (0, -2) and (2, -8).
As the inequality sign is ≤, draw a solid line through the plotted points and shade below the line.
SolutionThe solution set is the set of points contained within the overlapping shaded region and on the solid line.
Therefore, a point in the solution set is (-5, -5).
Select the correct answer.
What is the equation of the parabola shown in the graph?
The equation for the parabola in the graph is the one in option C:
y = (-1/4)x² -2x - 7
Which is the equation of the parabola?Remember that a parabola with leading coefficient a and a vertex (h, k) can be written as:
y = a*(x - h)² + k
Here the vertx is at (-4, -3), then:
y = a*(x + 4)² - 3
And we can see that it passes through the point (0, -7), replacing that we will get:
-7 = a*(0 + 4)² - 3
-7 = a*16 - 3
-7 + 3 = a*16
-4 = a*16
-4/16 = a
-1/4 = a
The quadratic is:
y = (-1/4)*(x + 4)² - 3
Expanding that, we will get:
y = (-1/4)x² -2x - 4 - 3
y = (-1/4)x² -2x - 7
The correct option is C.
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need help can someone help me
Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;
Statement Reason
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
∠BCA ≅ ∠DCA Congruent angles of a triangle (SAS).
AC ≅ AC Reflexive property
ΔABC ≅ ΔADC AAS postulate
What is an angle bisector?In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.
By applying the angle bisector theorem to the given triangle, the variable y can be calculated by using the following mathematical equation (formula):
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can logically deduce that ∠BCA is congruent to ∠DCA
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