24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.
Let x ounces of 15% alcohol must be mixed with the 16 ounces of 20% alcohol.
The amount of alcohol in 16 ounces solution is = (20/100) * 16 ounces
= 3.2 ounces
The amount of alcohol in x ounces solution is = (15/100) * x
= 0.15x ounces
Total amount of alcohol is = (16 + x) ounces
According to the problem we get an equation,
(3.2 + 0.15x)/(16 + x) = 17/100
100(3.2 + 0.15x) = 17(16 + x)
320 + 15x = 272 + 17x
320 - 272 = 17x - 15x
48 = 2x
x = 48/2
x = 24
Therefore, 24 ounces of a 15% alcohol solution must be mixed with 16 ounces of a 20% alcohol solution to make a 17% alcohol solution.
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Convert .51 kg to milligrams using unit fractions
The conversion of .51 kg to milligrams using unit fractions is given by 510,000 mg
How to convert from kilograms to milligrams?Units can be converted from one form to another.
Kilograms written as kg is a unit of massMilligrams written as mg is also a unit of mass.Convert kilogram to milligram:
1000g = 1 kg
1 kg = 1,000,000 mg
That is,
A kilogram is equivalent to one million milligrams.
.51 kg to milligrams
= .51 × 1,000,000
= 510,000 mg
Hence, the conversion of .51 kg to milligrams is 510,000 mg.
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The table shows the number of each type of cookie a
bakery has left at the end of the day. The baker wants to
make the greatest number of cookie boxes to sell, using
chocolate chip and sugar cookies together. If all of the
chocolate chip and sugar cookies are distributed evenly
among the boxes and the baker charges $5 per box, how
much money will the bakery bring in if they sell all of the
boxes?
A study is done on the number of bacteria cells in a petri dish. Suppose that the population site P(t) after t hours is given by the following. exponential function.
P(t)=2800(1.07)⁺
Find the initial population size
Does the function represent growth or decay?
O groats O decay
By what percent does the population size change each hour?
The initial population size is 2800
The function represents growth
The percentage through which the population size changes is given as 7%.
How to solve for the percentage growthThe formula is given as
[tex]Po = 2800 (1.07)^t[/tex]
From the formula that we have above, the initial population size is given as 2800.
We have p = P₀(1 + r)^t
where 1 + r = 1.07
We are to find the value of r
r = 1.07 - 1
r = 0.07
Given that the value of r is positive, this is the representation of a growth.
The percentage through which the change would occur = 0.07 x 100
= 7%
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How to find standard deviation using the range of the sample set?
The range of the data divided by four gives the standard deviation, which is approximately.
How do you find the sample standard deviation from the range?The range of the data divided by four gives the standard deviation, which is approximately. Simply put, that's it. To determine the range, find the highest value—the maximum—and deduct the lowest—the minimum. The range should then be divided by 4.
The range rule states that a sample's standard deviation is roughly equal to one-fourth of the data range.
In order to calculate the standard deviation, we must first determine the mean, take this mean away from each data point, square the differences, add them, divide by one less than the number of data points, and (at the very end) take the square root. The range rule, however, only needs one division and one subtraction.
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)
The time taken for the rocket to reach its maximum height as required in the task content is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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The expression −290+18y represents a submarine that began at a depth of 290 feet below sea level and ascended at a rate of 18 feet per minute. What was the depth of the submarine after 6 minutes?
Answer: would be -120 + 78, or -42 feet.
Step-by-step explanation:
If f(x) = x + 4 and g(x) = x2 + 6x + 8, what is f(x) divided by g(x)?
Answer:
[tex]\frac{x+4}{8x+8}[/tex]
Answer: 1/(x+2)
Step-by-step explanation:
[tex]\frac{x+4}{x^2+6x+8}\\[/tex]
[tex]\frac{x+4}{(x+2)(x+4)}[/tex]
the x+4 cancel each other so we are left with 1/(x+2)
if the main question was how to foil the denominator x2 + 6x + 8, i can quickly explain that.
x2 + 6x + 8
a2 + bx + c
first step is to multiply the first variable with that last or a * c which in this case would give 1 * 8 = 8
the next step would be to look at the middle number which is b, in our case 6.
so then you look for two number that can multiply to to give 8 as well as add up to 6. With easy guessing one will come up with 4 and 2.
with this values you can impute them directly into the equation as
x^2 +4x +2x+ 8
split the equation then factor
(x^2 +4x) (2x+ 8)
x(x+4) 2(x+4) note that the factored equation must always be the same in the bracket. If they are not the same then you have made a mistake somewhere across the line.
with the results giving (x+2)(x+4)
How do you calculate p-value from z-score?
The procedure to calculate the p-value from z-score depends on one of two choices: one-tailed (which may be Left-tailed or Right-tailed) or two-tailed tests.
How to calculate p-value from z-score?A z-table, otherwise termed the standard normal table, provides the area under the curve to the left of a z-score.
The technique for using z-tables to find p-values depends on the test being carried out; which may be; one- or two-tailed test.
For one-tailed tests, the directionality is also a factor.
It therefore follows that;
For a Left-tailed z-test: the p-value = Φ(Zscore)
For a Right-tailed z-test: the p-value = 1 - Φ(z-score).
For a Two-tailed z-test: the p-value = 2 * Φ(−|z-score|).
The procedure described above represents how to calculate p-value from z-score.
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The following formulas can be used to determine the p-value from its corresponding z-score
Left-tailed test: Φ(z-score)Right-tailed test: 1 - Φ(z-score)Two-tailed test: 2Φ(−|z-score|)How to calculate p-value from its z-score?From the question, the parameters are given as
p-valuez-scoreAlso, from the question, we understand that:
The p value depends on the z-score for its own value
There are three types of test for z-score; these test are:
Right tailed testLeft tailed testTwo tailed testThe p-value would assume different value for a z-score when the type of test is different
This means that the p value for z = 0.2 at right tail test is different at a left tailed test.
This means that there are three formulas for calculating the p-value from the z-score, and these formulas are
Left-tailed test: Φ(z-score)Right-tailed test: 1 - Φ(z-score)Two-tailed test: 2Φ(−|z-score|)Read more about p-value at
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3) Helen has $1.35 in her bank of nickels and dimes. There are 9 more nickels than dimes. Find the number she has of each kind.
Yesterday, you entered into a futures contract to sell 62,500 at $1.50 per . Your initial performance
bond is $1,500 and your maintenance level is $500. At what settle price will you get a demand for additional
funds to be posted?
The settle price at which you will get a demand for additional funds to be posted is $1.4840 per €.
What is contract?
An agreement between parties that results in legal duties for both parties is known as a contract. Mutual consent, demonstrated by a valid offer and acceptance, sufficient consideration, capability, and legality are the fundamental components needed for the agreement to be a legally enforceable contract.
Provided data from the question;
Futures contract to buy in euros = €62,500
Future contract to buy in dollar = $93,750 ( €62,500 × $1.50)
Initial performance of bond = $1,500
Maintenance level = $500
To determine the settle price at which you get a demand for additional funds to be posted =
Future contract to buy in dollar - (initial bond performance - maintenance level) ÷ future contract to in euros
$93,750 - ($1,500 - $500)
= $93,750 - $1,000
$92,750 ÷ €62,500
= $1.484
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Solving -8 + x > -9 for x is: x > -1.
True
False
Step-by-step explanation:
Solving -8 + x > -9 for x is: x > -1.
-8 + x > -9
add 8 to both sides:
-8 + x + 8 > -9 + 8
x > -1
True
i need help asap with this question
Answer:
-8/9
Step-by-step explanation:
(-7/9) /( (-1 1/6) * (-3/4) ) make all fractions improper fractions
(-7/9) / (-7/6 * -3/4) solve brackets
(-7/9) / (7/8)
(-7/9) * (8/7)
-8/9
Which phrase represents this expression? (6242) x 3 O 3 times the difference of 42 and 62 O the difference of the product of 3 times 42 and 62 O the difference of 62 and the product of 3 times 42 O 3 times the difference of 62 and 42.
By using the concept of mathematical expression, it is obtained that
(62−42)×3 is represented by 3 times the difference between 62 and 42
First option is correct
What is mathematical expression?
A mathematical expression consist of numbers connected with addition, subtraction, multiplication and division.
Here the given mathematical expression is (62−42)×3
Here, the signs shown are subtraction and multiplication. So the concept of difference and times will be used here
(62−42)×3 means whole of (62 - 42) is multiplied with 3
So, this is 3 times the difference between 62 and 42
First option is correct
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Correct Question
Which phrase represents this expression?
(62−42)×3
a) 3 times the difference of 62 and 42
b) 3 times the difference of 42 and 62
c) The difference of 62 and the product of 3 times 42
d) The difference of the product of 3 times 42 and 62
How to simplify this expression: 5-2(x+5)+2
Answer:
........
Step-by-step explanation:
...
....
.....
......
.......
Graphing and Solving Inequalities
m-1<-3
a
-4y <-20
5+b>1
-18
There is a graph underneath each one with lines and arrows.
The solution to inequalities are as follows.
What is inequality equation?
Inequalities are the mathematical expressions during which either side don't seem to be equal. In difference, in contrast to in equations, we tend to compare 2 values. The equal sign up between is replaced by but (or but or equal to), larger than (or larger than or equal to), or not capable sign.
Main body:
A) m-1 <-3
to solve this we need to take link terms to one side
= m< -3+1
= m < -2
B) -4y <-20
cancelling -ve sign on both sides,
= 4y <20
= y <5
C) 5+b>1
take link terms to one side
b > -4
Hence the graph is as given
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x^2+8x+y^2+8y-112=0 center and radius
We can rewrite the equation of the circle as:
(x + 4)^2 + (y + 4)^2 = 12^2
So the center is (-4, -4) and the radius is 12 units.
How to find the center and radius of the circle?For a circle of radius R and center (a, b) the equation is:
(x - a)^2 + (y - b)^2 = R^2
Here we have the equation:
x^2 + 8x + y^2 + 8y - 112 = 0
We can complete squares to get:
(x^2 + 8x) + (y^2 + 8y) - 112 = 0
(x^2 + 2*4*x + 4^2) + (y^2 + 8y + 4^2) - 4^2 - 4^2 - 112 = 0
(x + 4)^2 + (y + 4)^2 = 112 + 16 + 16 = 144
(x + 4)^2 + (y + 4)^2 = 12^2
So we have a circle of radius of 12 units, with a center at (-4 , -4)
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Write in slope intercept form.
Answer:
y=4x
Step-by-step explanation:
y2-y1/x2-x1
8-4/2-1
4/1
4 is the slope
We can find the intercept by finding when x is equal to zero by continuing the order pairs
(8,2),(4,1),(0,0)
The intercept is 0
Y=mx+b
M-slope
b- y intercept
hopes this helps please mark brainliest
A rectangle has a width represented by the expression-2x+20.The length of the rectangle is 6 more than twice the width.which expression represents the area of the rectangle?
Answer:
8(x^2)+172x+920
Step-by-step explanation:
width=2x+20length=2(width)+62(2x+20)+6
=4x+46
area=lenght ×width(4x+46)×(2x+20)
=4x(2x+20)+46(2x+20)
=8(x^2)+80x+92x+920
=8(x^2)+172x+920
Raina needs to earn at least $2200 each month to cover her living expenses. Her income comes from a 4% commission that she earns on everything she sells. What is the minimum amount she needs to sell in order to earn $2200?
The person needs to sell a minimum amount of $550000 to earn $22000.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the income of the person is 4% of the total selling value.
Let the person sells $x to earn $22000, therefore,
4% of x is $22000
Or, 4x/100 = 22000
4x = 2200000
x = 550000
Hence, the person needs to sell a minimum amount of $550000 to earn $22000.
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What is the first term of the quotient of the following division problem?
(x³ - 1) = (x + 2)
O -0.5
O 1
O x²
Ox^4
The solution to the algebraic problem is [tex]x^{2}[/tex]
What is an Algebraic Equation?
An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.
Solution:
([tex]x^{3}[/tex] – 1) = (x+2)
On dividing ([tex]x^{3} - 1[/tex]) by (x+2)
The first term of the quotient will be x^2 by following the Long Division Method of Algebraic Division.
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how to simplify (3x)³+2x³
Answer: 5x³
Step-by-step explanation:
What is the F ratio in ANOVA?
Answer:
The F value is used in analysis of variance (ANOVA). It is calculated by dividing two mean squares. This calculation determines the ratio of explained variance to unexplained variance. The F distribution is a theoretical distribution.
Step-by-step explanation:
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The F ratio in ANOVA is the difference between two mean square values. If
In ANOVA, what is the F ratio?Analysis of variance is a collection of statistical models and the estimation procedures that go with them that are used to analyze the differences between means. Ronald Fisher, a statistician, invented ANOVA. The ANOVA test compares more than two groups at the same time to see if there is a relationship between them.
If the null hypothesis is correct, you should expect F to be close to 1.0 most of the time. A high F ratio indicates that the variation among group means is greater than would be expected by chance.
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Differentiate the function with respect to x. Shot steps
The differentiated form of the function with respect to x will be e³ˣ³.9x².
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range. The exponential function is that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x where a is a constant and a>1.
It is given that the function is,
y=e³ˣ³
Differentiate the function with respect to x.
[tex]=\frac{dy}{dx} \\\\ =\frac{d}{dx}\left(\left(e^3\right)^{x^3}\right) \\\\ =e^{3x^3}\frac{d}{dx}\left(3x^3\right) \\\\ =e^{3x^3}\cdot \:9x^2[/tex]
Thus, the differentiated form of the function with respect to x will be e³ˣ³.9x².
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PLEASE HELP ASAP!!! Solve the problem.
Triangle KAP = triangle __ by rule __
Step-by-step explanation:
Statements Reasons
1. AK - angle bisector 1. Given
2. FP perpendicular AK 2. Given
3. <FAK congr <PAK 3. Definition angle bisector
4. Seg AK congr seg AK 4. Congr of seg's is reflexive
5. <AKF & <AKP are rt. angles 5. Def perpendicular lines
6. <AKF is congr <AKP 6. Thrm: Right angles are congr.
7. Triangle KAF congr triangle KAP 7. ASA
8. A_F = A_P 8. Corresp parts of congr tr are
congr
Simplify the expression. 11z +9-7=
Answer: 11z+2
Step-by-step explanation:
Question 3.13R:
Which of the following are equivalent exponential function(s) to f(x)=(4/7)^−x
The equivalent function of the exponential function is (a) f(x) = (7/4)ˣ
How to determine the equivalent function?From the question, we have the following function that can be used in our computation:
f(x) = (4/7)^-x
This function can be properly expressed as
f(x) = (4/7)⁻ˣ
Solving further, we need to apply the exponent law of indices
This is represented as
a⁻ˣ = 1/aˣ
When the above rule is applied, we have
f(x) = 1/(4/7)ˣ
Evaluate the quotient
f(x) = (7/4)ˣ
Hence, the equivalent is (a) f(x) = (7/4)ˣ
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What is the coefficient in this expression?
3/2
xy
Ox
OY
in this equation ox is your answer.
Determine the length of the line segment shown. line segment from negative 5 comma 5 to 3 comma negative 1
6 units
8 units
10 units
36 units
The distance of the line segment from ( -5,5 ) to ( 3,-1 ) is 10 units
What is the distance of a line between 2 points?
The distance of a line between 2 points is always positive and given by the formula
[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
Given data ,
Let the two points be A and B
A ( x₁ , y₁ ) = A ( -5 , 5 )
B ( x₂ , y₂ ) = B ( 3 , -1 )
So , the distance between 2 points is given by the formula
[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
Substituting the values of x₁ , y₁ , x₂ , y₂ in the formula , we get
[tex]D = \sqrt{(-5-3)^{2} + (5-(-1))^{2} }[/tex]
[tex]D = \sqrt{(8)^{2} + (6)^{2} }[/tex]
[tex]D=\sqrt{(64+36)}[/tex]
[tex]D = \sqrt{100}[/tex]
[tex]D= 10 units[/tex]
Hence , the distance of the line is 10 units
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Compute the amount in an account after 4 years if $4550 is invested at an annual interest rate of 3.5% compounded semiannually. Round to two decimals.
Answer:
$5,227.41
Step-by-step explanation:
The compound interest formula is
[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]
A is the final amount
P is the initial amount
r is the interest rate as a decimal
n is the # of times the interest is applied per time period
t is the # of time periods.
We are given
Note: semi annually is twice per year.
[tex]P=4550[/tex]
[tex]r=0.035[/tex]
[tex]n=2[/tex]
[tex]t=4[/tex]
Lets solve for A.
[tex]A=4550(1+\frac{0.035}{2} )^{2*4}[/tex]
[tex]A=4550(1.0175)^{8}[/tex]
[tex]A=4550(1.14888178)[/tex]
[tex]A=5227.41211244[/tex]
Round to two decimals.
$5,227.41
Question 36 of 50
When graphing systems of inequalities, the possible answers are all the points that are in the overlapped, shaded region of the two lines.
True
False
The solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. the region of overlap called the intersection.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
Thus, the solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. the region of overlap called the intersection.
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