Let
x -----> the number of milliliters of the 3.5% solution
y ----> the number of milliliters of the 6% solution
we have that
3.5%=3.5/100=0.035
6%=6/100=0.06
5%=5/100=0.05
so
0.035x+0.06y=0.05(500) -------> equation A
and
x+y=500 -----> x=500-y ------> equation B
solve the system of equations
substitute equation B in equation A
0.035(500-y)+0.06y=0.05(500)
solve for y
17.5-0.035y+0.06y=25
0.025y=25-17.5
0.025y=7.5
y=300
Find out the value of x
x=500-300=200
therefore
the number of milliliters of the 3.5% solution is 200 mlthe number of milliliters of the 6% solution is 300 mlSimplify by combining like terms. Type the termsin alphabetical order.-7a-2y+7+2y+5a=
-7a - 2y + 7 + 2y + 5a
Reordering:
(-7a + 5a) + (-2y + 2y) + 7 =
= -2a + 7 =
= 7 - 2a
help it’ll be greatly appreciated :(
In population 1:
Pattern is changing by 13.5 to 11.5 to 8.3
Which is 2 then 3.2.
In population 2:
Population is decreasing by 2.
Describe pattern.A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Given.
Pattern in which population is changing are:
In population 1:
It is changing by 13.5 to 11.5 to 8.3
Which is 2 then 3.2.
In population 2:
Population is decreasing by 2.
Completing the table:
Population 1 Population 2
42.8 29
38.6 27
33.4 25
27.2 23
Graph is mentioned below.
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So what's in the photo is what I need help with.
Answer:
1 == B No Solutions
2 == A One Solution
3 == C Infinitely Many Solutions
Explanation:
We first find go through each system and see which has one solution, no solutions, and infinitely many solutions.
1.
x
ng waffles for breakfast. The recipe calls for 1/2 cups of water for every 2Jemina pancake mix. How many cups water would he need for only oneake mix? Show your work
Ratio:
cups of water / pancake mix = (1/2) / 2
For 1 pancake mix, x cups of water:
x / 1 = (1/2) / 2
Solve for x, cross multiply:
2x = ( 1/2) 1
2x = 1/2
Divide both sides by 2
2x/2 = (1/2) / 2
x = 1/4
Answer:
She would need 1/4 cups of water
Transforming the graph of a quadratic, cubic, square root, or absolute value function
Explanation:
If we have a function g(x) = -f(x), then g(x) will be f(x) reflected across the x-axis.
If g(x) = f(x) - c, g(x) will be f(x) shifted c units down
If g(x) = f(x + c), g(x) will be f(x) shifted c units to the left.
In this case, the initial function is f(x) = |x| and g(x) = -|x + 3| - 2, then
g(x) = -f(x + 3) - 2
Therefore, g(x) will be the initial function reflected across the x-axis, shifted 3 units to the left and 2 units down.
Answer:
So, the graph for y = -|x + 3| - 2 will be:
rounded to the nearest tenth, what is the area of rectangle ABCD?
Given the rectangle ABCD, you can identify that it is divided into two Right Triangles:
[tex]\begin{gathered} \Delta ACD \\ \Delta ABD \end{gathered}[/tex]• You can find the length of the rectangle by applying the following Trigonometric Function:
[tex]\cos \alpha=\frac{adjacent}{hypotenuse}[/tex]In this case, you can set up that:
[tex]\begin{gathered} \alpha=30\degree \\ adjacent=CD=AB=l \\ hypotenuse=AD=9 \end{gathered}[/tex]Then, substituting values and solving for "l", you get:
[tex]\begin{gathered} \cos (30\text{\degree})=\frac{l}{9} \\ \\ 9\cdot\cos (30\text{\degree})=l \\ \\ l=\frac{9}{2}\sqrt[]{3}ft \end{gathered}[/tex]• In order to find the width of the rectangle, you can use this Trigonometric Function:
[tex]\sin \alpha=\frac{opposite}{hypotenuse}[/tex]In this case, you can say that:
[tex]\begin{gathered} \alpha=30\degree \\ opposite=AC=BD=w \\ hypotenuse=AD=9 \end{gathered}[/tex]Therefore, substituting values and solving for "w", you get:
[tex]\begin{gathered} \sin (30\degree)=\frac{w}{9} \\ \\ 9\cdot\sin (30\degree)=w \\ \\ w=\frac{9}{2}ft \end{gathered}[/tex]• Now you need to use the following formula for calculating the area of a rectangle:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width.
Substituting the length and the width of the given rectangle into the formula and evaluating, you get:
[tex]A=(\frac{9}{2}\sqrt[]{3}ft)(\frac{9}{2}ft)[/tex][tex]A\approx35.1ft^2[/tex]Hence, the answer is: Option C.
If y = 2x2 – 4, what is its inverse?
The inverse of the function y = 2 · x² - 4 is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4. (Correct choice: B)
How to find the inverse of a function
In this problem we have a quadratic function, whose inverse has to be found. First, we make the following substitution on the function:
y = x
x = y⁻¹
Now we proceed to clear y⁻¹ by using algebra properties:
x = 2 · (y⁻¹)² - 4
x + 4 = 2 · (y⁻¹)²
(x + 4) / 2 = (y⁻¹)²
√[(x + 4) / 2] = y⁻¹
y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4
The inverse of the function is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4.
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what is a root of a parabola?
The roots of a prabola is where the function intersects the x-axis.
What are the X and Y intercepts for the graph shown in the picture?
Based on the given figure, you can conclude:
x-intercepts:
x = 0
x = number in between 100 and 125, approximately 105
x = number greater than 175, approximately 180
y-intercepts:
y = 0
For the second and third x-intercepts there is no possible to specifiy the exact numbers due to the scale units of the graph.
If 3 gallons of paint are needed for 75 ft of fence, how many gallons are needed for 1200 ft of fence?
Answer:
48 gallons of paint are needed.
Step-by-step explanation:
Set up a proportion.
Like this: x is for the unknown number of gallons.
[tex]\frac{3}{75} = \frac{x}{1200}\\ 75(x)= 3(1200)\\ 75x=3600\\x= 3600/75\\x= 48 Answer[/tex]
Simplify. DO NOT PUT ANY SPACES IN YOUR ANSWER. - 3\4 (16r-24)
Explanation
[tex]-\frac{3}{4}(16r-24)[/tex]Step 1
eliminate the parenthesis applyng distributive property
[tex]\begin{gathered} -\frac{3}{4}(16r-24) \\ \frac{-3\cdot16r}{4}+\frac{3\cdot24}{4} \\ \frac{-48r}{4}+\frac{72}{4} \\ -12r+18 \end{gathered}[/tex]I hope this helps you
5x+2y=10 Does the relation represents a function
Answer:
Yes, it is a linear function. For every input there is only 1 output.
Step-by-step explanation:
Solve the inequality and graph the solution on the line provided. 9 + 3x ≥ -6
9 + 3x ≥ -6
9 is adding on the left, then it will subtract on the right
3x ≥ -6 - 9
3x ≥ -15
3 is multiplying on the left, then it will divide on the right
x ≥ -15/3
x ≥ -5
Write the conditional
statement in if-then form.
The vertices of a triangle
are not colinear.
The conditional statement for "The vertices of a triangle are not collinear" is "if the points are not collinear then they are vertices of triangle."
What is conditional statement?Conditionals are commands used in programming languages to handle choices. Particularly, conditionals carry out various calculations or actions based on whether a boolean condition defined by the programmer evaluates to true or false.
What is if-then?The hypothesis is a prediction of what will transpire in your experiment. The words "IF" and "THEN" are frequently used when writing the hypothesis. For instance, "I will fail the test if I don't study." Your independent and dependent variables are reflected in the "if" and "then" statements.
"The vertices of a triangle are not collinear" has a conditional statement that reads, "If the points are not collinear, then they are vertices of the triangle."
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What do the 2 points on the graph mean in terms of the situation
Coordinates - A pair of integers that show the location of a point on a graph. The first number represents the x-axis, while the second represents the y-axis.
Other names for this type of pair are ordered pair and numbered pair. A proportionate connection is one in which the values are all connected by the same constant value. A proportionate connection is also known as a linear relationship in mathematics.
Assume f(x) and g(x) are two functions that accept a real number as input and return a real number as output.
The intersection points of f(x) and g(x) are then those x values for which f(x)=g(x).
The precise numbers can sometimes be discovered by algebraically solving the equation f(x)=g(x).
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At the market, 5 light bulbs cost $9
How much do 7 light bulbs cost?
what is 5 to the 6 power written in expanded form
5 to the 6th power is:
[tex]5^6[/tex]This, written in expanded form, is:
[tex]5\cdot5\cdot5\cdot5\cdot5\cdot5[/tex]Question is in the photo.
The derivative of y = [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
What is a derivative of a function?The derivative of a function f(x) represents its rate of change.
We have,
y = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex]
Putting log on both sides.
[ log a² = 2 log a ]
log y = 1/2 log [tex]\frac{x(x+4)}{(5x+1)(3x+7)}[/tex]
log y = 1/2 [ log x(x+4) - log (5x +1)(3x + 7) ]
log y = 1/2 [ log x(x+4) - log(5x + 1) - log (3x + 7) ]
Derivation on both sides.
[ d(logx)/dx = 1/x ]
d (log y) / dx = d [ {1/2 log x(x+4) - log(5x + 1) - log (3x + 7)} ] / dx
1/y y' = 1/2[ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]
y' = y/2 [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
Thus,
The derivative of y = [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
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In december 2004 35% of student in the high school were satisfied with the lunches supplies through the school of the 856 survey, 265 inducted they were satisfied does this suggests the proportion of student satisfied with the quality of lunches has decreased
What does it means to make a type 2 error for the test
When one fails to reject a null hypothesis that is actually wrong, this error is known statistically as a type II error. This term is used in the context of hypothesis testing.
A type II error, often called an error of omission, results in a false negative. When the patient is infected, a disease test, for instance, can return a negative result. This is a type II error because, despite being wrong, we accept the test's negative conclusion.
The difference between a type I and type II error is that a type I error refers to the failure to reject a valid null hypothesis, whereas a type II error refers to the failure to do so. Despite the fact that the error does not happen by accident, it rejects the alternative theory.
The likelihood of mistakenly failing to reject the null hypothesis when it does not apply to the entire population is known as a type II error.
In essence, a type II error is a false negative.
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Suppose a triangle has sides a, b, and c, and that a² + b² < c². Let 9 be the
measure of the angle opposite the side of length c. Which of the following
must be true? Check all that apply.
A. The triangle is not a right triangle.
B. cose < 0
C. cose > 0
□ D. a² + b²-c² = 2abcose
SUBMIT
Using trigonometry we know that option (B) "cosθ < 0" is correct.
What is Trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.For a right-angle triangle, the sum of the square of the legs is equal to the hypotenuse side(longest side).
Therefore, for a right triangle
a² + b² = c²For the triangle that has a² + b² > c², it shows it is not a right triangle.
Let θ be the measure of the angle opposite the side of length c.We have to find the statements which are must be true.Cosine law:
c² = a² + b² - 2abcosθSubstitute the value then we get:
c² < c² - 2abcosθSubtracting c² on both sides of the inequality:
c² - c² < c²- c² - 2abcosθ0 < -2abcosθAdding 2abcosθ on both sides then we get:
2abcosθ < -2abcosθ + 2abcosθ = 02abcosθ < 0cosθ < 0cosθ is negative in the second quadrant and third quadrants.
Therefore, using trigonometry we know that option (B) "cosθ < 0" is correct.
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4) Find mZUVW if mZNVW = 61° mZUVW= 15x – 5, and mZUVN= 10x – 11. 15 5x 5
a bond issue outstanding that matures in 19 years. The bonds pay interest semiannually. The bonds have a face value of $1,000 and are currently priced at $995.28. The bonds carry a coupon rate of 3.5 percent. What is the aftertax cost of debt if the total tax rate is 22 percent? Multiple Choice
The after tax cost of debt for the bond is 2.73%
Given,
The face value of the bond, FV = $1000
Present value of the bond, PV = $995.28
Maturity period = 19 years
Coupon rate = 3.5%
Total tax rate = 22%
We have to find the after tax cost of debt for the bond.
The bond pays interest semiannually ;
so coupon rate = 3.5/2 = 1.75
Coupon payment , pmt= 0.0175 x 1000 = $17.5
Maturity, nper = 19 years x 2 = 38
Compute yield rate using spreadsheet = Rate(nper,pmt,-PV, FV)
Then,
= RATE(38, 17.5, -995.28, 1000)
Rate or yield is computed as 3.5%
The present value is negative as it is a cash outflow.
The cost of debt is 3.5%
The tax rate is 22%
After tax cost of debt = 3.5 (1 - 0.22) = 2.73%
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Describe a series of transformations Matt can perform to device if the two windows are congruent
Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.
What are transformation ?There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.
We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.
Matt has the following transformational abilities:
Reflection (Flip)
A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.
Rotations as a Congruence Transformation
Rotations as a Congruence Transformation
A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. A rotation must include indicate the clockwise or counterclockwise direction. This information can be used to calculate the degree, quantity, and direction of a revolution.
Translational congruence transformation
We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.
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Please help solve this.
Answer:
C
Step-by-step explanation:
[tex]x^2 - 2x - 1 = 0\\x^2 = 2x + 1\\x^4 = 4x^2 + 4x + 1\\x^4 = 4(2x + 1) + 4x + 1\\x^4 = 8x + 4 + 4x + 1\\x^4 = 12x + 5[/tex]
The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks plus $125 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function.
C (n) = 6500 + 125n
(a). What is the total cost of transporting 12 tons?
(b). If the total cost is $9375, how many tons is the company transporting?
The total cost of transporting 12 tons is $8000 and number of tons the company transporting is 23.
The total cost of transporting 12 tons can be calculated by keeping the value of number of tons in the formula.
Total cost = 6500 + 125×12
Performing multiplication on the Right Hand Side of the equation
Total cost = 6500 + 1500
Performing addition on the Right Hand Side of the equation
Total cost = 8000
The number of tons can be calculated by keeping the total cost in the formula.
9375 = 6500 + 125n
125n = 9375 - 6500
Performing subtraction on Right Hand Side of the equation
125n = 2875
n = 2875 ÷ 125
Performing division
n = 23
So, the total cost is $8000 and number of tons is 23.
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A survey showed that of college students read internet news on a regular basis and that of college students regularly watch the news on TV. The survey also showed that of college students both follow TV news regularly and read internet news regularly.
(a)What is the probability that a student watches TV news regularly, given that he or she regularly reads internet news? Round your answer to the nearest hundredth.
(b)What is the probability that a randomly selected college student reads internet news regularly, given that he or she watches TV news regularly? Round your answer to the nearest hundredth.
For the given values, the probability that a student watches TV news regularly is 0.833, the probability that a randomly selected college student reads internet news regularly is 0.240.
According to a survey, 83% of college students routinely watch the news on television, while 24% of college students read newspapers on a regular basis.
Additionally, the survey revealed that 20% of college students routinely read newspapers and watch TV news.
(A) Given that a student reads newspapers frequently,
The answer is [P(TV and newspapers)/P] where P(watches TV|reads newspapers) (newspapers)
= 0.20/0.24 = 0.833
(b) Given that a randomly chosen college student watches TV news frequently
The answer is that P(newspapers | watches TV) = [P(newspapers and TV)] / P. (TV)
= 0.20/0.83 = 0.240
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Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. The tax rate t that maximizes revenue for the government is 66.992%.
Tax rate that maximizes revenueRevenue can be defined as the amount or the income a person or an organization generated from the sales of goods and services.
Given function :
Total sale = S(t) = 7−6∛t
Hence,
Expression for Revenue rate = r(t) = tS(t)
Now let substitute and solve expression
r(t) = t (7−6∛t)
= 7t−6(t)^4/3
Differentiate the expression
d[r(t)] dt = r′(t)
r′(t) = 7− (4/ 3) 6(t)^1/3
=7−8(t) ^1/3 ........ expression (1)
Maximum revenue
r′(t) = 0
Substitute and solve expression (1)
0 =7−8(t)^1/3
(t) = (7/8)^3
= 0.66992 × 100
= 66.992%
Therefore we can conclude that the tax rate t that maximizes revenue is 66.992%.
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The complete question is :
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
S(t)=7−6∛t
standard deviation for binomial distribution n=48 p=3/5
If a standard deviation for binomial distribution n = 48 p = 3/5 . The standard deviation is 3.39.
What is the Standard deviation?Using this formula to determine or find the standard deviation for the binomial distribution
σ =√np(1−p)
Where:
n = 48
p = 3 / 5 or 0.6
σ = ?
Let plug in the formula so as to determine the standard deviation
σ =√ (48) (0.6) ( 1 - 0.6)
σ =√ (48) (0.6) (0.4)
σ =√ 11.52
σ = 3.39
Therefore we can conclude that 3.39 is the standard deviation.
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21. Complete the following transactions and explain how they would appear in your register.
(5 points each - 2 points for the correct answers and 3 points for a correct explanation of your
process)
• You open your bank account on April 16 with a tax refund check of $145.00.
You pay Sell Phone $65.34 on April 18. (Check 794)
• You deposit your paycheck on April 23. ($9.76 hour for 35 hours)
• You buy $61.32 (4% sales tax not included) in clothes from BargainsRUs on April 24
using your debit card.
Be sure to include in your response:
.
• the steps you followed to complete your computations
the balance as of April 24
• the process for entering the transaction in the registry
(5 points)
After all the transaction, money left in the bank account is $15.8872.
Given that, you open your bank account on April 16 with a tax refund check of $145.00. You pay Sell Phone $65.34 on April 18.
What is a tax refund check?A tax refund is a reimbursement to a taxpayer for any excess amount paid to the federal government or a state government.
On April 16th balance in the account = $145.00 cost of phone = $65.34 on April 18.
Balance on April 18 = 145.00-65.34
= $79.66
Deposited check $9.76 on 23rd April for 35 hours
Balance on 23rd April = 79.66+9.76
=$89.42
Since, the check deposited only for 35 hours, again balance on 24th April will be $79.66
On 24th April you brought clothes from BargainsRUs for
61.32+4% of 61.32
= 61.32+2.4528
= $63.7728
So, the remaining balance in the account = 79.66-63.7728
=$15.8872
Therefore, after all the transaction, money left in the bank account is $15.8872.
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Serum albumin levels in adults are distributed approximately Normally with a mean of 35 g/l and a standard deviation of 5 g/l. What is the probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l? (Enter your answer rounded to two decimal places.)
There is a 0.6915 = 69.15% probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented below:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.The mean and the standard deviation of the albumin levels are given as follows:
[tex]\mu = 35, \sigma = 5[/tex]
The probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l is one subtracted by the p-value of Z when X = 32.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (32.5 - 35)/5
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
1 - 0.3085 = 0.6915 = 69.15% probability.
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