For the solution of the inequality -3x - 7 < 20 to be shown graphically, we need to solve it first and then graph the solution.
\(\begin{gathered} -3x-7<20 \\ C\text{ ollecting like terms}, \\ -3x<20+7 \\ -3x<27 \\ \text{Dividing both sides by -3, the inequality sign changes when multiplied or divided by a negative number.} \\ x>\frac{27}{-3} \\ x>-9 \end{gathered}\)Hence, the graph that shows the solution x > -9 is the second graph from the options. Option B
What is the greatest common factor of 15 and 10?
Answer:
5
Step-by-step explanation:
Answer:
5 is the right answer...I hope this helps you :)
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose ? = 2.7 and ? = 220.(a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to four decimal places.)
at most 250, less than 250, more than 300.
(b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.)
(c) What value is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.)hr
Answer:
Step-by-step explanation:
Given that
\(\alpha =2.5\) ,\(\beta =220\)
The weibull distribution with parameters \(\alpha \ \ and \ \ \beta\)
where \(\alpha =0 \ \ , \beta =0\)
\(F(x,\alpha ,\beta) \left|\begin{array}{cc}\frac{\alpha }{\beta } x^{\alpha-1e^-(x/\beta)^\alpha &x\geq 0\\0&x<0\end{array}\right\)
Then,
\(F(x,\alpha ,\beta )=\left|\begin{array}{cc}0&x<0\\1-e^-^{(x/\beta)}^\alpha &x\geq 0\end{array}\right\)
A) The probability that a specimen's lifetime is at most 250 is
\(P(X\leq 250)=F(250,2.7,220)\\\\=1-e^-^(250/220)^{2.7}\\\\=1-0.2436\\\\=0.7564\)
The probability that the specimen's life time is more than 300 is
\(P(X>300)=1-P(X\leq 300)\\\\=1-F(300;2.7,220)\\\\=1-(1-e^-^{(300/220)^{2.7}\)
\(=e^-^{(300/220)^{2.7}\)
= 0.0992
b)The probability of the specimen's lifetime is between 100 and 250
\(P(100<X<250)=P(X<250)-P(X<100)\\\\=F(250;2.7,220)-F(100;2.7,220)\\\\=(1-e^-^{(250/220)^2^.^7})-(1-e^-^{(100/220)^2^.^7})\\\\=(1-0.2436)-1(1-0.8878)\\\\=0.6442\)
c) The value such that exactly 50% of all specimens have lifetimes exceeding that value is
\(P(X>x)=0.50\\\\1-P(X<x)=0.50\\\\1-(1-e^-^{(x/220)^{2.7}}=0.50\\\\e^-^{(x/220)^{2.7}}=0.50\\\\-(x/220)^{2.7}=In(0.50)\\\\(x/220)^{2.7}=-In(0.50)\\\\(x/220)=[-In(0.50)]^{(\frac{1}{2.7})} \\\\x=220[-In(0.50)]^{(\frac{1}{2.7})}\)
x = 192.07
Patty's dog weighs 48 ounces. How many pounds does Patty's dog weigh?
Answer:
If Patty's dog weighs 48 ounces, and we convert ounces to pounds, our answer is 3. Patty's dog weighs 3 pounds
Step-by-step explanation:
Please help me! (this is from khan academy 6th grade math!)
Answer:
1st → 1st
2nd → 3rd
3rd → 2nd
Step-by-step explanation:
just divide the first set of student wishes to the second set of students in the same question. the 1st for example
x-ray to all students is 6/ 36= 1/6 = 1:6
for all students, you add all the students in the table
Answer:
1st=1st
2nd=3rd
3rd =2nd
Step-by-step explanation:
basic math
The piecewise function represents the amount of taxes owed, f(x), as a function of the taxable income, x. Use the marginal tax rate chart or the piecewise function to answer the questions.
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
A piecewise function f of x in seven pieces. The function is defined by part 1, which is 0 point 10 times x for x less than or equal to 10,275; part 2, which is 0 point 12 times x minus 205 point 50 for 10,276 is less than or equal to x which is less than or equal to 41,175; part 3 which is 0 point 22 times x minus 4,323 for 41,176 is less than or equal to x which is less than or equal to 89,075; part 4 which is 0 point 24 times x minus 6,105 point 50 for 89,076 is less than or equal to x which is less than or equal to 170,050; part 5 which is 0 point 32 times x minus 9,070 point 32 for 170,051 is less than or equal to x which is less than or equal to 215,950; part 6 which is 0 point 35 times x minus 26,187 point 50 for 215,951 is less than or equal to x which is less than or equal to 539,900; and part 7 which is 0 point 37 times x minus 36,985 point 67 for x is greater than or equal to 539,901.
Part A: Using the method of your choice, demonstrate how to calculate the amount of taxes owed on a taxable income of $31,000. Show all work. (4 points)
Part B: Using the taxes owed from part A, determine the effective tax rate. Show all work. (4 points)
Part C: Compare the piecewise function to the marginal tax rate chart. How is the marginal tax rate chart represented in the piecewise function? (2 points)
Answer:
Part A: $3,415.50
B: 11.34%
Step-by-step explanation:
Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50
Part B: For the effective tax rate, divide the amount in part A by the taxable income
Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.
To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.
Explanation:Part A:
To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:
f(x) = 0.12 * 31000 - 205.50 = $3,574.50
Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.
Part B:
To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:
Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%
Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.
Part C:
The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.
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Identify the range of the function shown in the graph.
Answer:
Identify the range of the function shown in the graph.
Answer:
range=(10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10)
Multiply.
(b - 7)(2b +9)
(b - 7)(2b + 9) = (Simplify your answer.)
Answer:
foil method
add/subtract like terms
Step-by-step explanation:
b×2b=2b²
b×9=9b
-7×2b=-14b
-7×9=-63
-14b+9=-5
=2b²-5b-63
What is the missing statement in the proof? Scroll down to see the entire proof. a ∠BDC≅∠ADB b ∠BCA≅∠DCB c ∠BAC≅∠BAD d ∠DBC≅∠BAC
The missing statement in the proof specified is given by: Option B: ∠BCA≅∠DCB
What is the reflexive property of congruence?
According to the reflexive feature of congruence, the geometric quantity under consideration—be it an angle, a line segment, a form, etc.—is congruent to itself.
The third step's key concept in this instance is the "Reflexive Property of Congruence."
The fourth phase comes to the conclusion that the ΔABC~ΔBDC criteria for similarity are met.
Since it was established in the second stage that ∠ABC≅∠BDC
Therefore, in order for the fourth step to apply angle-angle similarity, which requires the angles of two considered triangles to be congruent, we must demonstrate another angle pair of triangles ΔABC and ΔBDC being congruent in the third step.
Internal angle C is the common angle in the triangles ABC and BDC.
As a result, it is consistent with itself due to its reflexive characteristic.
We obtain the following notation for internal angle C from triangle ABC:
Angle ACB and BCA(both will work)
Triangle BDC gives us the following notation for internal angle C:
Angle DCB and BCD(Both will function.)
They fit together. The second choice takes angle C into account, so:
∠BCA≅∠DCB (second option) is the missing statement.
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O U N U Size of Cryst.
Answer:
They can occur for various reasons, and they may need different treatments.
Step-by-step explanation:
you have 1400 square feet of boards to use for a new tree house. Design a tree house that has a volume of at least 250 cubic feet.
A total of 6 sheets, or 1403.55 square feet of plywood is required.
EquationsAssuming the treehouse is a rectangular prism, we can use the formula for the volume of a rectangular prism to find the dimensions of the treehouse:
Volume = length x width x height
We want the volume to be at least 250 cubic feet, so let's set the height to be 5 feet:
250 = length x width x 5
length x width = 50
We also know that the surface area of the treehouse should be 900 square feet. The surface area includes the floor, walls, and roof, so we can break it down as follows:
Surface area = area of floor + area of four walls + area of roof
Surface area = lw + 2lh + 2wh
Substituting 5 for h and 50/w for l, we get:
900 = 50w + 10w + 500/w
Simplifying and solving for w, we get:
Using a numerical solver, we find that w ≈ 4.37 feet.
Using this value of w, we can solve for l and h:
l ≈ 11.45 feet
h = 5 feet
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Solve the following equation. Then place the correct number in the box provided. 2x - 1 ≤ x + 5
\(\huge\textbf{TheStarryNights }\)Hi There!
Solve the Inequality:
2x-1≤x+5
Move all the variables (in this case, x's) to the left, using the opposite operation:
2x-x-1≤5
Move -1 to the left:
2x-x≤5+1
Combine like terms:
x≤6 (Answer)
Hope it helps & enjoy your day!\(\huge\textbf{TheStarryNights}\)
Arif’s grandfather is 9 times as old as Arif. Which of these could be the age of Arif’s grandfather?
Select all the equations that are equivalent to y-4 =2/3(x-1)
The equivalent equations of y - 4 = 2/3(x - 1) are y - 4 = 2/3x - 2/3 and y = 2/3x + 10/3
How to determine the equivalent equation?From the question, we have the following parameters that can be used in our computation:
y - 4 = 2/3(x - 1)
We start by expanding the bracket
So, we have the following representation
y - 4 = 2/3x - 2/3
Next, we add 4 to both sides of the equation
This gives
y - 4 + 4 = 2/3x - 2/3 + 4
Evaluate the like terms
So, we have the following representation
y = 2/3x + 10/3
Hence, the equivalent equation is y = 2/3x + 10/3
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i need serious help someone pleaseeeee
The value of c in the polynomial is - 7.
How to solve polynomials?The polynomial is given as follows:
p(x) = 2x³ - x² + cx + 2 . The value of c if x - 2 is a factor of p(x) can be computed as follows:
Therefore,
p(x) = 2x³ - x² + cx + 2
when x - 2 is a factor, p(x) = 0
Therefore,
0 = 2x³ - x² + cx + 2
Hence,
2(2)³ - (2)² + 2c + 2 = 0
16 - 4 + 2c + 2 = 0
12 + 2 + 2c = 0
2c = - 14
divide both sides by 2
c = - 14 / 2
c = - 7
Therefore,
c = -7
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A jewelry company ordered 10 boxes of glass beads. There were 30 beads in each box. How
many glass beads did the jewelry company order?
glass beads
Answer:
300 glass beads
Step-by-step explanation:
There are 30 beads in each box so you multiply 30 by 10.
\(10*30=300\)
Roland’s family drove 4 and 6/10 km from their home they home to the gas what is the maximum number of days that Carl can feed his dog exactly 2 and 1/2 cups of dog food from one full bag
According to the question 560 cups divided by 20 cups per week equals 28 weeks.
What is divided?Division is a mathematical operation that involves splitting a number or quantity into equal parts. It is an essential process in mathematics, used to solve problems and find solutions. Division involves dividing a number, or a set of numbers, by another number. The result of the division is known as the quotient. Division can also be used to find fractions or ratios, as well as to divide a number into its parts.
Assuming the bag of dog food is a large bag and Carl is feeding his dog 2 1/2 cups daily, the maximum number of days Carl can feed his dog from one full bag is 28.
This is because 2 1/2 cups equals 20 cups per week, and a large bag typically contains approximately 560 cups.
Therefore, 560 cups divided by 20 cups per week equals 28 weeks.
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The entire number of kilometres driven by Roland's family can be determined by using the phrase \(=\frac{69}{10}\)
How to calculate Distance?To determine the total number of kilometres driven by Roland's family, the distance from their home to the gas station and the distance from the gas station to the shop must be added.
There are \(4\times \frac{6}{10}\) kilometres between their home and the gas station, which can also be stated incorrectly as follows:
\(4\times \frac{6}{10}=\frac{(4\times 10+6)}{10} \\\\=\frac{46}{10}\)
The formula for expressing the distance between the gas stop and the store is 2 30/100 kilometers, which can be written as follows:
\(2\times\frac{30}{100} =\frac{(2\times100+30)}{100} \\\\=\frac{230}{100}\)
To calculate the overall distance traveled, we add the two distances:
\(\frac{46}{10} +\frac{230}{100}\)
To combine these fractions, we need to find a common denominator. Only one unique digit, 100, can be used to divide both 10 and 100. In light
of this, we can rewrite the equation as follows using 100 as the common denominator:
\((\frac{46}{10} )\times (\frac{10}{10} )+(\frac{230}{100} )\times (\frac{1}{1} )\)
That amounts to:
\(\frac{46}{100} +\frac{230}{100} =\frac{690}{100}\)
Therefore, we can reduce this fraction by multiplying the numerator and denominator by their ten largest common factor:
\(\frac{690}{100} =\frac{(69/10)}{(100/10)} \\\\=\frac{69}{10}\)
Consequently, the phrase that follows may be used to determine the overall number of kilometres driven by Roland's family:
\(2\times\frac{30}{100} +4\times \frac{6}{10} =\frac{69}{10}\ km\)
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Rest of the question is,
They drove 2 30/100 kilometers from the gas station to the store. Which expression can be used to determine the number of kilometer Ronald's family drove altogether.
Given Sin A = 5 /√34 and that angle A is in Quadrant I find the exact value of sec A in simplest radical form using a rational denominator
The given function is
\(\sin A=\frac{5}{\sqrt[]{34}}\)We know that secA is the inverse of cosA.
From the given function, we form the following triangle
Because the sine function is equivalent to the ratio between the opposite leg and the hypotenuse.
So, let's use the Pythagorean's theorem to find y
\(\begin{gathered} c^2=a^2+b^2 \\ (\sqrt[]{34})=y^2+5^2 \\ 34=y^2+25 \\ y^2=34-25 \\ y=\sqrt[]{9} \\ y=3 \end{gathered}\)Once we have the adjacent leg, we can express the cosine function
\(\cos A=\frac{3}{\sqrt[]{34}}\)Then, the inverse is
\(\sec A=\frac{\sqrt[]{34}}{3}\)Hence, the secA function is\(\sec A=\frac{\sqrt[]{34}}{3}\)Lesson 17: Use the Four Operations to Solve Problems Cool Down: Andre's Balloons Andre has 125 balloons. He and 4 friends hung up some balloons for a party at school and now there are 80 balloons left. If each person hung up the same number of balloons, how many balloons did each person hang up? 1. Write an equation with a letter for the unknown quantity to represent the situation. 2. Solve the problem. Explain or show your reasoning.
a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.
b) An equation representing the situation is x = (125 - 80)/5.
What are the mathematical operations?The four basic mathematical operations include addition, subtraction, division, and multiplication.
The mathematical operations provide solutions to mathematical problems using operands.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
The total number of balloons that Andre has = 125
The number of balloons remaining after hanging some for the school party = 80
The difference (number of balloons used) = 45 (125 - 80)
The number of friends who hang the balloons = 5
The number of balloons hung by each friend of Andre = 9 (45/5)
Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.
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In which quadrant is the point (-2, -9)?
Answer:
3rd quadrant
Step-by-step explanation:
Given:
Point (-2, -9)
Computation:
In 1st quadrant (+ , +)
In 2nd quadrant (- , +)
In 3rd quadrant (- , -)
In 4th quadrant (+ , -)
So given point (-2, -9) is in 3rd quadrant.
Find one value of x for which h(x)=4 and find h(4)
Adam is a team leader for a packing and moving company. Today, his team packed 72 boxes in 4 hours. What was his team's packing rate, in boxes per hour?
A.
20 boxes per hour
B.
18 boxes per hour
C.
21 boxes per hour
D.
17 boxes per hour
Answer: 18 boxes per hour
Step-by-step explanation:
72 divided by 4 is 18
Which is true about
parallel planes?
A. They are planes that do not intersect.
B. They are coplanar and intersect.
C. They are planes that intersect.
Answer:
The answer is a, they are planes that do not intersect
4. P/E Ratios. Favorita Candy’s stock is expected to earn $2.40 per share this year. Its P/E ratio is 18. What is the stock price? (LO7-1)
Answer:
2.4*18 = $43.2
stock price is $43.2
Step-by-step explanation:
Find the constant rate of change for each linear function and interpret its meaning
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
and to get it, we simply need two points off of the straight line, hmm let's use the ones in the picture below.
\((\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}\)
*NEED HELP I WILL GIVE BRAINLIEST FOR BEST ANSWER PLEASE HELP ME*
A cylinder has a height of 9 meters and a diameter of 36 meters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
______cubic meters
Answer:
0.15 cubic meters
Step-by-step explanation:
Formula volume = π x radius² x height
Answer
πr2h
Step-by-step explanation:
What do 12y and 8y represent? You can look up the formula for the volume of a cylinder pir^2h and plug in your dimensions.
Provide the correct reason for the statement in line 2.
Answer:
you can ask to your teacher for help
Solve for w |w|=6 I have HW and I need help
\(w=\sqrt{6},\sqrt{-6}\)
What is modulus ?
A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the output is always favourable. The equation is y = |x|.
Given:
\(w|w|=6\\w(-w)=6\)
or
\(w(w)=6\)
solving both one by one,
\(w(-w)=6\\-w^{2} =6\\w=\sqrt{-6}\)
and,
\(w(w)=6\\w^{2} =6\\w=\sqrt{6}\)
\(w=\sqrt{6},\sqrt{-6}\)
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Brenda has four more nickels than quarters in her purse. She has a total of $3.80 in change and a $200 in Nordstrom gift cards. How many nickels does she have? ASAP
Answer:
16 nickelsStep-by-step explanation:
GivenNickel n = 5 cQuarter q= 25 cTotal change = $3.80 = 380 cn = q + 4Solution5n + 25q = 3805(q + 4) + 25q = 380 ⇒ substitute n with q + 45q + 20 + 25q = 38030q = 360q = 360/30q = 12n = q + 4 = 1612 quarters
16 nickels
Can someone help solve this please ?
Answer:
it's the third one bc I got it right
Star A is approximately 4.2 × 1013 kilometers away. Star B is approximately 6.3 × 1015 kilometers away. About how many times as far away is star B as star A?