Answer:
instead of x < -4 it should be x > -4
Step-by-step explanation:
7x - 20x < 52
subtract 20x from 7x which is -13x
now the equation is -13x < 52
divide both sides by -13 but when you divide by a negative you switch the sign so it would x > -4 not x < -4
hope this helps :)
A certain loan program offers an interest rate of 4.5%, compounded continuously. Assuming no payments are made, how
much would be owed after six years on a loan of $1300?
Do not round any intermediate computations, and round your answer to the nearest cent.
$
X 5
?
0
00
B
The principal amount of $2,287.26 from compound interest at a rate of 4.5% per year owed after six years on a loan of $1300
Since n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually, sothe final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
Given that certain loan program offers an interest rate of 4.5%, compounded continuously.
Assuming no payments are made so;
First, convert R as a percent to R as a decimal
r = R/100
r = 4.5/100
r = 0.045 per year,
Then, solve the equation for P
P = A / (1 + r/n)^nt
P = 1300/ (1 + 0.045 /365)(365)^(15)
P = 1300/ (1 + 0.00010137)^(4745)
P = $2,287.26
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Audio Button Question The volume of a cylindrical container is 251 cubic inches. The radius of the container is 4 inches. Find the height of the container. Round your answer to the nearest inch.
The height of the cylindrical container is approximately 5 inches.
What is the height of the cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given that:
Volume V = 251 cubic inches
Radius r = 4 inches
Height h = ?
Plug the given values into the above formula and solve for height.
V = π × r² × h
251 = 3.14 × 4² × h
251 = 3.14 × 16 × h
251 = 50.24 × h
h = 251/50.24
h = 5 inches.
Therefore, the measure of the height is 5 inches.
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If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 1/4, what are the odds against a direct hit?
A)3 to 1
B)1 to 3
C)1 to 4
The odds against a direct hit is 3 to 1.
Given that the probability of a hurricane hitting at a coast is 1/4 = 0.25.
Therefore, the probability of not hitting = 1-0.25
= 0.75
we know that,
Odds against direct hit = [P(no direct hit)]/P[(direct hit)] = 0.75/0.25 = 3/1
= 3:1
Hence the odds against a direct hit is 3 to 1.
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Franklin Lyons is married and claims 3 withholding allowances. He gets paid overtime if he works over 40 hours in a week. His gross pay is $958.38. Find the Federal Withholding Tax.
Based on the assumptions, the estimated Federal Withholding Tax for Franklin Lyons would be approximately $191.68.
Determine Franklin's taxable income:
To calculate the taxable income, we need to subtract any deductions or exemptions from his gross pay. We'll consider his gross pay as the taxable income.
Taxable Income = Gross Pay = $958.38
Estimate the Federal Withholding Tax rate:
The Federal Withholding Tax rate depends on the taxable income and the individual's filing status. Let's assume a general tax rate of 20% for this estimation.
Federal Withholding Tax rate = 20%
Calculate the Federal Withholding Tax:
To find the withholding tax, multiply the taxable income by the tax rate:
Federal Withholding Tax = Taxable Income * Federal Withholding Tax rate
= $958.38 * 0.20
= $191.68
Thus, the answer is $191.68.
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Describe the translation shown using a table of values and an algebraic rule.
Help please
The algebraic rule for the translation in this problem is given as follows:
(x,y) -> (x + 9, y - 1).
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.Comparing the equivalent vertices, the translations for this problem are given as follows:
9 units right.1 unit down.Hence the algebraic rule for the translation in this problem is given as follows:
(x,y) -> (x + 9, y - 1).
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lan is 1.83m tall
Donna is 6cm shorter
What is Donna's height in metres?
Answer:
Step-by-step explanation:
lan is 1.83m tall. Donna is 6cm shorter. What is Donna's height in metres? 1.77m. Bath. √34°. 20m. 11m. 11x14. Work out the range. 3 8 4 8 3 5 9. 9-3=6.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x is 9.
Given,
Trapezoid with two bases and median.
base 1 = 44
base 2 = 2x + 10
median = 36
Now,
In trapezoid two bases will be parallel to each other.
Median = 1/2(sum of two bases)
From the formula of median the value of x will be,
Median = 1/2( base 1 + base 2 )
Substitute the values,
36 = 1/2( 44 + 2x + 10 )
72 = 54 + 2x
x = 9
Hence both the bases of trapezoid are obtained.
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Need the answer for first picture!
The measure of <MNL is (71 - 3x²)/2.
We have,
Far Arc = 59 - 2x²
Near Arc = 12 - x²
Angle = 180- 2x²
Using the Formula
Angle= Average of vertical chords
180 - 2x² = (59 - 2x² + 12 - x²)/2
360 - 4x² = 71 - 3x²
289 = x²
x= 17
So, the measure of <MNL
= (71 - 3x²)/2
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Suppose a new postoperative procedure is administered to a number of patients in a large hospital. The researcher can ask the question, Do the doctors feel differently about this procedure from the nurses, or do they feel basically the same way? Note that the question is not whether they prefer the procedure but whether there is a difference of opinion between the two groups.
To answer this question, a researcher selects a sample of nurses and doctors and tabulates
the data in table form, as shown. Use a significance level of 5%.
To determine whether there is a difference of opinion between doctors and nurses regarding a new postoperative procedure, the researcher conducted a survey and tabulated the data in a table form. The next step is to analyze the data using statistical methods and a significance level of 5%.
To begin the analysis, the researcher can use a statistical test such as the chi-square test for independence. This test will examine whether there is a significant association between the opinions of doctors and nurses regarding the procedure.
The chi-square test will compare the observed frequencies in each category (e.g., doctors who feel differently, doctors who feel the same, nurses who feel differently, nurses who feel the same) with the frequencies that would be expected if there was no association between the profession and opinion.
If the calculated chi-square value exceeds the critical value at a significance level of 5%, it suggests that there is a significant difference in opinion between the two groups.
The researcher should calculate the chi-square value, degrees of freedom, and compare it to the critical value from the chi-square distribution table.
If the calculated chi-square value exceeds the critical value, the researcher can conclude that there is a significant difference of opinion between doctors and nurses regarding the postoperative procedure.
It is important to note that statistical significance does not imply practical significance. Even if there is a significant difference, the magnitude of the difference should be considered in the context of the study.
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The radius of a circle is 17 centimeters. What is the circle's circumference?
Answer:
The circle's circumference is approximately 106.81 centimeters.
Explanation:
The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the circle.
So, for a circle with a radius of 17 centimeters, its circumference can be found by:
C = 2πr
C = 2 x 3.14 x 17
C ≈ 106.81 cm
Therefore, the circumference of the circle is approximately 106.81 centimeters.
please please please please answer
The value of the variable t of the exponential equation [tex]-5\cdot e^{10\cdot t} = - 30[/tex], t = (1 / 10) · ㏑ 6 (EXACT), t = 0.179 (APPROXIMATE).
How to solve an exponential equation
In this problem we need to clear the variable t of an exponential equation with one variable, this can done by means of relationship of exponential and logarithmic functions, logarithm properties and algebra properties.
Now we proceed to present the complete procedure for the solution to the exponential equation:
[tex]-5\cdot e^{10\cdot t} = - 30[/tex]
[tex]e^{10\cdot t} = 6[/tex]
10 · t = ㏑ 6
t = (1 / 10) · ㏑ 6
t = 0.179
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The mean of a, 31, 42, 65, and b is 51. The greatest number is 67 more than the least number. What are the missing numbers? Please explain.
Answer:
a=25
b=92
Step-by-step explanation:
Because the average of the five numbers is 51, the sum of the five numbers is 255.
a+b+73+65=255
138+a+b=255
a+b=117
a+67=b
Therefore,
a=25
b=92
Feel free to tell me if I made a mistake! :)
Can you solve the hcf of 20and 10
The HCF (highest common factor) of 20 and 10 is 10.
To determine the 20 and 10's highest common factor (HCF).
We must identify the highest number that can divide both 20 and 10 without producing a remainder in order to determine the HCF.
1, 2, 4, 5, 10, and 20 are the variables that make up 20.
1, 2, 5, and 10 make up the number 10.
The biggest element that both 20 and 10 have as a shared component is 10.
The HCF of 20 and 10 is hence 10.
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A restaurant makes smoothies in batches of 12.5 litres.
The smoothies are made from ice cream and a mixed fruit
juice in the ratio 3 : 2.
34% of the juice is apple juice.
Work out the maximum number of batches of smoothie that
can be made from 51 litres of apple juice.
Answer: If 34% of the mixed fruit juice is apple juice, then 66% of it is a combination of other fruit juices. We can assume that the ratio of apple juice to other fruit juices remains the same in the ice cream and mixed fruit juice mixture.
Let the volume of ice cream in each batch be 3x litres and the volume of mixed fruit juice be 2x litres. Then the total volume of mixture in each batch is 5x litres.
If 34% of the mixed fruit juice is apple juice, then the volume of apple juice in each batch is 0.34 × 2x = 0.68x litres. The volume of other fruit juices in each batch is 2x − 0.68x = 1.32x litres.
The ratio of ice cream to mixed fruit juice is 3 : 2, so we have:
3x : 2x = ice cream : mixed fruit juice
Simplifying, we get:
ice cream = 1.5 × mixed fruit juice
Substituting the values we obtained earlier, we have:
3x = 1.5 × 2x
x = 0.75
Therefore, the volume of ice cream in each batch is 3x = 2.25 litres, and the volume of mixed fruit juice is 2x = 1.5 litres.
To make 1.5 litres of mixed fruit juice, we need 0.68 litres of apple juice and 0.82 litres of other fruit juices.
To make 12.5 litres of smoothies, we need 2.25 litres of ice cream and 10.25 litres of mixed fruit juice. Of this, 0.68 litres is apple juice and 9.57 litres is other fruit juices.
Therefore, to make 12.5 litres of smoothies, we need 0.68/1.5 × 12.5 = 5.67 litres of apple juice.
To make 51 litres of apple juice, we can make a maximum of 51/5.67 ≈ 9 batches of smoothies.
please help i don’t feel like typing
Answer: q=13
Step-by-step explanation:
add the separate the q, add 4 to the 9= 13
13=q
The surface area of this cylinder is 20,761.68 square yards. What is the height?
Use ≈ 3.14 and round your answer to the nearest hundredth.
29 yd
h=
Submit
h
yards
The height of the cylinder whose surface area is given would be = 85 yards.
How to calculate the height of a cylinder?The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.
To calculate the height of a cylinder, the formula that should be used is given as follows:
Surface area of cylinder = 2πrh + 2πr²
radius = 29 yards
surface area = 20,761.68 square yards
height = ?
That is ;
20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29
20,761.68 =182.12h + 5281.48
182.12h = 20,761.68-5281.48
182.12h = 15480.2
h = 15480.2/182.12
= 85 yards
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Find the surface area of the composite solid to the nearest hundredth.
A composite solid of a square prism with a square pyramid extending from the top and bottom face of the prism. The width, length, and height of the prism are all 5 inches. The slant height of the pyramid on the bottom of the prism is 7.5 inches. The height of the pyramid on top of the prisim is 3 inches.
The surface area of the composite solid is 255 square inches.
How to find the surface area of the composite solid?We will compute the surface area of each component and then add them together to find the surface area of the composite solid.
First, the surface area of the square prism:
Given: The square prism has a width, length, and height of 5 inches each.
Formula for the surface area of a rectangular prism: 2lw + 2lh + 2wh
Surface area of the prism = 2(5 * 5) + 2(5 * 5) + 2(5 * 5)
= 2(25) + 2(25) + 2(25)
= 50 + 50 + 50
= 150 square inches
Next, the surface area of the square pyramid at the bottom:
Given: The slant height of the pyramid on the bottom of the prism = 7.5 inches.
The base of the pyramid is a square with a side length of 5 inches.
Formula to find the lateral surface area of a square pyramid: (perimeter of base) * slant height / 2.
The base is a square, the perimeter is 4 times the side length.
Lateral surface area of the bottom pyramid = (4 * 5) * 7.5 / 2
= 20 * 7.5 / 2
= 150 / 2
= 75 square inches
Then, the Surface area of the square pyramid at the top:
Given: The height of the pyramid on top of the prism = 3 inches.
The base of the pyramid is a square with a side length of 5 inches.
Lateral surface area of the top pyramid = (4 * 5) * 3 / 2
= 20 * 3 / 2
= 60 / 2
= 30 square inches
Finally, we shall find the total surface area by summing up the surface areas of each component in this way:
Total surface area = Surface area of the prism + Surface area of the bottom pyramid + Surface area of the top pyramid
= 150 + 75 + 30
= 255 square inches
Therefore, the surface area of the composite solid = 255 square inches.
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The parabola y = x^2 is scaled vertically by a factor of 1/10
The parabola y = x² scaled vertically by a factor of 1/10 gives y = x²/10
Calculating the image of the vertical scaleFrom the question, we have the following parameters that can be used in our computation:
The parabola y = x² is scaled vertically by a factor of 1/10
The rule of this transformation is
Image = (x, ay)
Where
a = 1/10
So, we have
y = 1/10 * x²
Evaluate
y = x²/10
Hence, the image of the function is y = x²/10
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The sales tax rate for the state of Washington was 9.2%.
a) What is the state sales tax on a $2,800 used car in Washington?
b) What is the final cost of the car, including tax?
a) The state sales tax on a $2,800 used car in Washington is given as follows: $257.6.
b) The total cost of the car, including tax, is given as follows: $3,057.6.
How to obtain the sales tax and the total cost of the car?The sales tax and the total cost of the car are obtained applying the proportions in the context of the problem.
The sales tax rate is given as follows:
9.2%.
Hence, for a car of $2,800, the sales tax is given as follows:
0.092 x 2800 = $257.6.
The total cost is then obtained adding the base cost to the sales tax, as follows:
2800 + 257.6 = $3,057.6.
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mara works for an electronics store and receives a 6.5% commission on her sales. She also recevies a weekly salary 460. mara's boss asks her to specialize in the sale of flat screen televisions that cost $414 each, which means those are the only items she will sell. write and sole an equation to find the number of televisions, t, she sells in one week if she earns 890.56 for the week
Answer:
16 tvs
Step-by-step explanation:
Maura's earnings for the week equal her weekly salary (460) plus she earns 6.5% commission x number of flat screens sold x $414.
So: Total Earnings = 460+ 0.065*414*t where t is the number of tvs she has sold.
If total earnings = 890.56, just substitute that above and solve for t.
890.56= 460+ 0.065*414*t
430.56=0.065*414*t
430.56=26.91*t
430.56/26.91 = t
16 = t
She sold 16 tvs to earn 890.56.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
6/MN = 8/9
8MN = 54
MN = 6 3/4
The correct answer is B.
last year a company made a profit of one and a quarter million dollars each year the company reinvests 1/3 of the profit how much of this profit will they reinvest
The amount of profit that will be reinvested is 5/12 million.
How much profit will be reinvested?Profit is the excess of revenue over cost.
Profit = revenue - total cost
In order to determine the profit that will be reinvested, multiply the fraction that is reinvested by the value of the profit.
Amount that will be reinvested = profit x fraction that is reinvested
1 1/4 x 1/3 =
5/4 x 1/3 = 5/12 million
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Question 4Mple Choice Worth 2 points)
Ares of Polygons and Composite Figures MC)
A composte figure is shown
024413
028.445²
1.15 in
Which of the following represents the total area of the figure?
010 663 ²
034.335 ²
4.6 in.
3h 563
P
The total area of the composite figure which has triangle and rectangle is 24.41 square inches
The given composite figure has two triangles and one rectangle
Area of rectangle =length × width
=4.6×3.15
=14.49 square inches
Area of left side triangle, it has base of 3.3 in and height 3.15 inches
Area of triangle = 1/2×3.3×3.15
=5.1975 square inches
Area of triangle on right side
Base = 3 in
Height = 6.3-3.15=3.15 in
Area of triangle = 1/2×3×3.15
=4.725 square inches
Total area = 14.49 + 5.1975 + 4.725
=24.41 square inches
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Find the value of x. Round to the nearest tenth .
Answer:
23.8
Step-by-step explanation:
In a right-angled triangle, x ² + b ² = c ²
30.5 is c, we can choose b to be 19.1.
x ² + b ² = c ²
x ² = c ² - b ²
= 30.5² - 19.1²
= 565.44
x = √565.44
= 23.8 (to 3 significant figures)
what’s is the surface area of this rectangular prism?
Answer:
220 in²
Step-by-step explanation:
surface area = [area of the 4 vertical faces] + area of the base + area of top.
surface area = [2(4 X 10) + 2(5 X 10)] + (4 X 5) + (4 X 5)
= (80 + 100) + 20 + 20
= 220 in²
What is the answer to this question.
Find the indicated values.
Arcs
mab
mabc
mbac
macb
The measures of the following arcs are :
m∡AB = 49°
m∡ABC = 253°
m∡BAC = 156°
m∡ACB = 311°
What is the explanation for this?Note that the sum total of the arcs in a circle is 360°
m∡AB = 49° - Given
m∡ABC = 360° 107° = 253°
m∡BAC = 107 + 49 = 156°
m∡ACB = 360 - 49 = 311°
A curve's arc length is significant because it represents the distance between two locations on the curve. The circumference of a circle is equal to its arc length. The arc length of an ellipse equals the ellipse's perimeter.
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John enclosed his 9 foot square garden. How much fence will he need
John will need 36 feet of fence to enclose his 9-foot square garden.
How much fence does John needs to enclose the garden?A sqaure is simply a polygon made up of four equal sides, with all the interior angles measuring 90 degrees.
The perimeter of a square is expressed as:
Perimeter = 4 × side length
Given that, the side length of the square garden is 9 ft.
To calculate the amount of fence John will need to enclose his 9-foot square garden, we need to determine the perimeter of the square.
Perimeter = 4 × side length
Plug in the side length
Perimeter = 4 × 9 ft
Perimeter = 36 feet
Therefore, the perimeter of the garden is 6 feet.
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What is the value of x?
Answer:
x = 9
Step-by-step explanation:
6/(x - 1) = 21/(3x + 1)
21(x - 1) = 6(3x + 1)
21x - 21 = 18x + 6
3x = 27
x = 9
Answer:
Step-by-step explanation:
To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
This helped me when i was learning to solve for x
Solve each equation by completing the square.
d² - 24d + c
Answer:
d² - 24d + c = (d - 12)² - 144 + c
Can someone answer this question?
The graph represents
[tex]{y \to -\infty}[/tex] as [tex]{x \to \infty}[/tex]
[tex]{y \to \infty}[/tex] as [tex]{x \to -\infty}[/tex]
From the given graph we can see that,
The curve represent cubic function
And we know that such cubic function is of the form
f(x) = y = -(ax³ + bx² + cx + d)
Since,
A function can approach two separate limits: one in which the variable approaches its limit by using values more than the limit, and one in which the variable approaches its limit by using values less than the limit.
Case 1:
Take limit of x approaching to infinity,
[tex]\lim_{n \to \infty} f(x) = y = -\infty[/tex]
Hence,
As x approaches to infinity the
y approaches to negative infinity.
Case 2:
Take limit of x approaching to negative of infinity,
Now since degree of function is 3 which is odd
Therefore,
[tex]\lim_{n \to -\infty} f(x) = y = \infty[/tex]
Hence,
As x approaches to negative infinity then
y approaches to infinity.
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