The inequality -4(x+3)<-2-2x simplifies to x > -5. Therefore, the number line representing this solution should shade the values greater than -5, thus, highlighting that x is any value greater than -5.
Explanation:Let's solve the inequality -4(x+3)<-2-2x step by step:
Distribute -4 through (x+3) to get -4x-12<-2-2x. Add 4x to both sides to isolate x, which leads to -12 < 2x - 2. Finally, add 2 to both sides to isolate x to get -10 < 2x or equivalently, x > -5.
As a result, the number line that represents this solution is one where the values greater than -5 are shaded. This means the value of x is anything greater than -5. Any number line visualization should start at -5 and include everything to the right of that point.
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Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
Hendrick makes birdhouses every weekend. it takes him 35 minutes to make a birdhouse. write and algebric expression that shows how long it takes him to make a birdhouse
At noon, ship a is 60 km west of ship
b. ship a is sailing south at 15 km/h and ship b is sailing north at 5 km/h. how fast is the distance between the ships changing at 4:00 pm?
The two ships are sailing in opposite sides, Hence, the resultant speed is given by 15+5 = 20 km/hr.
Therefore, from the below triangle, we have
[tex]\frac{dx}{dt} = 20 \text{ km/hr}[/tex]
Let the distance between the ships is y. On applying Pythagorous theorem, we have
[tex]y^2=x^2+60^2\\ \text{On differentiating, we get}\\ 2y\frac{dy}{dt} =2x\frac{dx}{dt}\\\frac{dy}{dt}= \frac{x}{y} \frac{dx}{dt}[/tex]
On substituting the value of y as [tex]y=\sqrt{60^2+x^2}[/tex]
[tex]\frac{dy}{dt} =\frac{x}{\sqrt{60^2+x^2}} \frac{dx}{dt}[/tex]
Since, the at noon the ship is 60 km to each other. Hence, for 4 PM, i.e. t=4, we have
[tex]x=4 \times \frac{dx}{dt} \\ x= 4 \times 20 \\x=80[/tex]
On substituting the value in above, we get
[tex]\frac{dy}{dt} =\frac{80}{\sqrt{60^2+80^2}} (20[/tex]
[tex]\frac{dy}{dt} = 16.0 \text{ km/hr}[/tex]
Therefore, the distance between the ships changing at a rate of 16 km/hr at 4:00 pm
The region r is bounded by the parabola y = x2 and the line y = 4. set up definite integrals to find the moment mx of r about the x-axis and the area a of the region r. then find (x, y )
Using synthetic division, find the quotient Q(x) and the remainder R if the polynomial P(x) = x3 − 2x2 − 3x + 18 is divided by (x + 2).
The quotient Q(x) is found to be x² - 4x - 11 and the remainder R is 4.
The question involves using synthetic division to find the quotient Q(x) and the remainder R when the polynomial P(x) = x³ − 2x² − 3x + 18 is divided by (x + 2).
To perform synthetic division, we first write down the coefficients of P(x): 1, -2, -3, and 18. The divisor is (x + 2), so we use -2 for the synthetic division.
Write the coefficients of P(x): 1, -2, -3, 18.
Write the root of the divisor (x + 2) = -2 on the left side of the synthetic division setup.
Bring down the first coefficient (1).
Multiply -2 by 1, place the result (-2) under the second coefficient (-2), and add the two numbers yielding -4.
Repeat the multiplication and addition process for the rest of the coefficients.
The results of the synthetic division process give us the coefficients of the quotient Q(x) and the remainder R.
In performing the synthetic division, we find that the quotient Q(x) is x² - 4x - 11 and the remainder is R = 4.
jeffery wei received a 6 year non subsidized student loan of 30000 at an annual interest rate of 5.2%. what are jeffery’s monthly loan payments for this loan after he graduates in 4 years
Jeffery's monthly loan payments for the loan will be $515.19.
Explanation:To calculate the monthly loan payments for Jeffrey, we can use the formula for calculating the monthly payment of a loan. The formula is:
Monthly Payment = (Principal * Monthly Interest rate) / (1 - (1 + Monthly Interest rate) ^ (-n))
In this case, Jeffrey's principal is $30,000, the annual interest rate is 5.2%, and the loan term is 6 years. Since Jeffrey will graduate in 4 years, we need to adjust the loan term accordingly. The monthly interest rate can be calculated by dividing the annual interest rate by 12, and the number of monthly payments will be multiplied by 4.
Using these values in the formula, we can calculate the monthly loan payment for Jeffrey.
Monthly Payment = (30000 * 0.052/12) / (1 - (1 + 0.052/12) ^ (-24))
Monthly Payment = $515.19
Add the opposite number of 1 1/5 to the sum of the numbers (−8 3/4 ) and (−2 5/6 ).
anaya drew a cylinder with a radius of 3 inches and a height of 5 inches. she also drew a cone with the same radius and height. which of the following is true?
A slice is made perpendicular to the base of a right rectangular prism as shown.
What is the area of the resulting two-dimensional cross section?
Drag and drop the answer into the box.
mm²
48
28
84
144
16
Answer:
The correct option is 1. The area of cross section area is 48 mm².
Step-by-step explanation:
From the find it is noticed that the cross section is a rectangle with length 4 mm and width is 12 mm.
The area of a rectangle is the product of its dimensions.
[tex]A=l\times w[/tex]
Where, l is length of the rectangle and w is width of the rectangle.
The area of cross section is
[tex]A=4\times 12[/tex]
[tex]A=48[/tex]
Therefore the area of cross section area is 48 mm². Option 1 is correct.
determine the area of a 21ft circle
Solve the equation
3/4=y−1/5 (8)
y=
Alicia buys a 5 pound bag of rocks for fish tank. She uses 1 1/8 pounds for a small fish bowl. How much is left
a parallelogram has an area of 108 square inches. The base of the parallelogram is 18 inches. Explain how you could find the height of the parallelogram, then find the height. Show your work.
Answer:
Height=6in
Step-by-step explanation:
Took test and got it correct
how much lower is Checkpoint 1 than Checkpoint 5?
checkpoint 1: -188
checkpoint 5: -57
the top of a hill rises 462 feet above Checkpoint 1. What is the altitude of the top of the hill?
checkpoint 1: -188
hill rises: 462ft
The altitude of the top of the hill is 274 feet.
To find how much lower Checkpoint 1 is than Checkpoint 5, we subtract the elevation of Checkpoint 1 from the elevation of Checkpoint 5:
Difference = Elevation at Checkpoint 5 - Elevation at Checkpoint 1
Difference = (-57) - (-188)
Now, simplify the expression:
Difference = -57 + 188
Difference = 131 feet
So, Checkpoint 1 is 131 feet lower than Checkpoint 5.
Next, to find the altitude of the top of the hill, we add the rise of the hill to the elevation at Checkpoint 1:
Altitude of the top of the hill = Elevation at Checkpoint 1 + Hill rise
Altitude = (-188) + 462
Now, calculate the sum:
Altitude = 274 feet
The altitude of the top of the hill is 274 feet.
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When 1 is added to the difference between seven times a number and 9, the result is greater than 10 added to 6 times the number. Find all such numbers.
One class of 75 students has an average midterm score of 67 and an sd of 12. another class of 325 students has an average of 72 and an sd of 15. find the average and the sd of the combined list of 400 students. hint: this uses the sd of a long list formula.one class of 75 students has an average midterm score of 67 and an sd of 12. another class of 325 students has an average of 72 and an sd of 15. find the average and the sd of the combined list of 400 students. hint: this uses the sd of a long list formula.
The average of the combined list of 400 students is 71.9 and the standard deviation is 13.1.
Explanation:To find the average and standard deviation of the combined list of 400 students, you can use the following formulas:
Average of combined list = (Average of one class * Number of students in one class + Average of another class * Number of students in another class) / Total number of students
Standard deviation of combined list = sqrt(((SD of one class)^2 * (Number of students in one class - 1) + (SD of another class)^2 * (Number of students in another class - 1) + ((Average of one class - Average of another class)^2 * Number of students in one class * Number of students in another class)) / Total number of students)
Applying the values from the given information:
Average of combined list = (67 * 75 + 72 * 325) / 400 = 71.9
Standard deviation of combined list
= sqrt(((12^2 * 74) + (15^2 * 324) + ((67 - 72)^2 * 75 * 325)) / 400)
= 13.1
One angle of a rhombus measures 108°, and the shorter diagonal is 9 inches long. Approximately how long is the side of the rhombus? (Hint: Diagonals of a rhombus bisect the angles.) 7 in. 8 in. 11 in.
Answer:
8 in.
Step-by-step explanation:
Let's find the rhombus's length...
cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]
cosine = ° = 54°
adjacent = = 4.5 in
Length of Rhombus = Hypotenuse
So...
cos54 = [tex]\frac{9}{x}[/tex]
x = [tex]\frac{4.5}{cos 54}[/tex]
x = 7.6558... about 8 inches
Sophia and Charlie brought potato salad to the company cookout. Sophia brought 2 quarts and Charlie brought 4 pints. How many TOTAL cups of potato salad did Sophia and Charlie bring together? (1 quart = 4 cups; 1 pint = 2 cups) A) 8 cups B) 10 cups C) 16 cups D) 20 cups
PLEASE HELP IM SO CONFUSED BY THIS
If the measure of angle ACB = 30 and the measure of angle A = 80, find the measure of angle B
A: 60
B: 110
C: 180
D: 70
If the measure of angle ACB = 30 and the measure of angle A = 80, the measure of angle B is 70 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
If the measure of angle ACB = 30 and the measure of angle A = 80, To find the measure of angle B
We know that the angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
∠ACB + ∠A + ∠B = 180
30 + 80 + ∠B = 180
∠B = 180 - 110
∠B = 70
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Why do clouds tend to form around 3:00 pm and 6:00 am
Two squares are attached to the sides of a quarter circle as shown. What is the best approximation for the area of this figure? Use 3.14 to approximate pi. 178.5 mm² 215.7 mm² 231.8 mm² 278.5 mm² Two squares with sides measuring 10 mm. Both squares are connected by a quarter circle.
Answer:
the answer is D
Step-by-step explanation:
A cookie recipe states for every 3 cups of flour, 1 1/2 teaspoons of vanilla are needed. How many teaspoons are needed for 5 cups of flour?
the digit in the __ place is the best stem value for the set of data shown above? please help
Using the mode concept, according to the stem-and-leaf plot, the missing value is of 71.
What is the mode of the data-set?It is the value that appears the most times in the data-set. When it's unique, the mode is the value that appears the most often in a data set and it can be used as a measure of central tendency, like the median and mean.
Here, we have,
In this problem, following the key format of the stem-and-leaf plot, disconsidering the missing value, the values 71 and 64 each appear 3 times.
However, the mode is 71, meaning that is should appear more times than 64, which means that the missing value is of 71.
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complete question:
This Stem-and-Leaf Plot is missing one data item. If the mode of the data set is 71, what is the value of the unknown data item?
Paul needs 40 pounds of 48% silver alloy to finish a collection of jewelry. How many pounds each of 45% silver alloy and 60% silver alloy should he melt together to obtain the alloy he needs
A geometric sequence is shown below : 2/3,2,6,18.. write the explicit formula
Lita,Kala, and Rose entered a typing competition. Lita typed 2 times as fast as Kala. The ratio of the number of words Kala typed to the number of words Rose typed was 4:1. If Rose typed 48 words, how many words did Lita type?
The IRS has a group of 45 tax returns, 15 of which contain errors. An IRS auditor randomly selects 3 tax returns from this group. What is the probability the auditor selects none of those containing errors? Round to four decimal places.
Answeeeeeerrrrr
0.2861
A prism with a base area of 3m^2 and a height of 4m^2 is dilated by a factor of 3/2 what is the volume of the dilated prism
Jacobs & Johnson, an accounting firm, employs 15 accountants, of whom 9 are CPAs. If a delegation of 4 accountants is randomly selected from the firm to attend a conference, what is the probability that 4 CPAs will be selected? (Round your answer to three decimal places.)
Using the hypergeometric distribution, it is found that there is a 0.0923 = 9.23% probability that 4 CPAs will be selected.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, there are 15 accountants, 9 are CPAs and 4 will be selected, hence N = 15, k = 9, n = 4.
The probability that 4 CPAs will be selected is P(X = 4), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,15,4,9) = \frac{C_{9,4}C_{6,0}}{C_{15,4}} = 0.0923[/tex]
0.0923 = 9.23% probability that 4 CPAs will be selected.
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53b−7b−6b+1 if b=25
Please help me with this problem! And what is the simplified expression?
Answer: 1001
B/c i said so