A company has recently been hiring new employees. today the company has 35% more employees than it did a year ago. if there are currently 37,800employees, how many employees did the company have a year ago?
Answer:
28000 employeeStep-by-step explanation:
let x be the number of the employees of the company ,a year ago.
the statement “today ,the company has 35% more employees than it did a year ago”
means
[tex]x+\frac{35}{100} x=37800[/tex]
[tex]\Longrightarrow x\times \left( \frac{100}{100} +\frac{35}{100} \right) =37800[/tex]
[tex]\Longrightarrow x\times \left( \frac{135}{100} \right) =37800[/tex]
[tex]\Longrightarrow x=\frac{37800\times 100}{135}[/tex]
[tex]\Longrightarrow x =28000[/tex]
441 N of force is being applied to the zip-lining seat that Sarah is sitting on. What is Sarah's mass?
Answer:
45 kg
Step-by-step explanation:
Formula for force :
Force = mass x gravity due to accelerationSolving :
441 N = mass x 9.8 m/s²mass = 441/9.8mass = 45 kgFind the surface area
Answer:
59.4
Step-by-step explanation:
Answer:
200.96 square feet
Step-by-step explanation:
SA = 2pi(r²) + 2pi(r)h
r = 2
pi = 3.14
h = 14
SA = 2(3.14)2² + 2(3.14)(2)14
SA = 6.28(4) + 6.28(2)14
SA = 25.12 + 175.84
SA = 200.96
You and your friend are in the studio audience of a television game show. the show randomly picks 2 people in the audience. if there are 300 people in the audience, what is the possibility of you and your friend being chosen
Answer:
2/300, or simplified: 1/150. Decimal: 0.006
Step-by-step explanation:
What is the simplest form of the expression below? f 2 − 25 5 × f f − 5
Answer:
[tex]{f}^{2} - 2f - 120[/tex]
Goodluck
help me with this math equation peez
Answer:
x = 15, 45 degree angle
Step-by-step explanation:
2x + 15 and 6x - 45 adds up to 90 degrees
(2x + 15) + (6x - 45) = 90
combine like terms:
2x + 6x = 8x
15 + (-45) = -30
8x - 30 = 90
8x - 30 + 30 = 90 + 30
8x = 120
8x / 8 = 120 / 8
x = 15
2(15) + 15
30 + 15 = 45 degree angle
6(15) - 45
90 - 45 = 45
Answer:
x = 15.
Step-by-step explanation:
The figure is a square so opposite sides are congruent and parallel.
The 2 angles marked are interior alternate angles, so they are congruent.
Therefore:
2x + 15 = 6x - 45
15 + 45 = 6x - 2x
4x = 60
x = 15.
orge needs to reflect a figure across the line y = negative 4. Which statements are correct regarding steps he could take to complete the reflection? Check all that apply.
Jorge should graph in the vertical line with values of –4 for the line of reflection.
Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection.
Jorge could count how far each vertex of the figure is from the y-axis and count the same distance on the other side.
Jorge will not move any point that lies on the line of reflection.
Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection.
Jorge could check his work by making sure that the image has the same orientation as the original.
The statement second, statement fourth, and statement fifth are correct as the reflection line is y = -4.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have:
Jorge needs to reflect a figure across the line y = -4
Here, y = -4 is a vertical line.
The correct statements regarding the steps he could take to complete the reflection are:
Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection.Jorge will not move any point that lies on the line of reflection.Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection.Thus, the statement second, statement fourth, and statement fifth are correct.
Learn more about the geometric transformation here:
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Kohl's needed to get her computer fixed she took it to the repair store the technician at the store worked on the computer for 6 hours and charged her $59 for parts. The total was $749.
Answer:
$115
Step-by-step explanation:
The cost of the labor per hour is $115.
The total amount that the technician charged her is the sum of the cost for the total hours worked and the costs of the parts.
Total charge = cost of total hours worked + cost of parts
$749 = $59 + cost of total hours worked
Cost of total hours worked = $749 - $59
Cost of total hours worked = $690.
Find the Volume and Surface area
Answer:
Volume: 203,594
Surface Area: 105,237
----------------------------------------------------------------------------------------------------------
Solve for surface area ✅Let's start with surface area because it is a bit complex.
[tex]A = 5 ah + \frac{1}{2} \sqrt{5(5 + 2 \sqrt{5})}~a^2[/tex]
Now, we must break all of these factors into an equation.
remember, the height is 4, the base is 172
[tex]A = 5 * 172 * 4 + \frac{1}{2} * \sqrt{5 * (5 + 2 * \sqrt{5})} * 172^2[/tex]
[tex]A = \sf 1.05237 * 10^5 = 105,237[/tex]
So that should wrap things up for surface area, being 105,237
________________________________________________________
Solve for volume ✅Now, we move on to the volume of this pentagonal prism.
[tex]A = \frac{1}{4} \sqrt{5(5 + 2 \sqrt{5})}~a^2h[/tex]
Similar to surface area, but different.
[tex]A = \frac{1}{4} * \sqrt{5 * (5 + 2 * \sqrt{5})} * 172^2 * 4[/tex]
And the result of this is...
[tex]A = \sf 2.03594 * 10^5[/tex]
Which is also equal to ⇒ 203,594
please let me know if this helped or was correct, I really spent a lot of time on this and would like to hear any good or bad feedback. Thanks!
The list shows the thickness of ice on the roads after a storm. On the line plot each x represents 1 measurement which line plot matches the data
Answer:
Step-by-step explanation:
Ice sheets have one particularly special property. They allow us to go back in time and to sample accumulation, air temperature and air chemistry from another time[1]. Ice core records allow us to generate continuous reconstructions of past climate, going back at least 800,000 years[2].
Ice coring has been around since the 1950s. Ice cores have been drilled in ice sheets worldwide, but notably in Greenland[3] and Antarctica[4, 5]. High rates of snow accumulation provide excellent time resolution, and bubbles in the ice core preserve actual samples of the world’s ancient atmosphere[6].
Find the slant height of a cone given that its lateral area is 144π cm2 and the diameter is 9 cm. diameter 9 cm 2 cm 32 cm 4 cm 18 cm
Answer:
32 cm.
Step-by-step explanation:
Lateral area = πrL
where r = radius of the base and L = the slant height.
The radius = 1/2 * diameter = 4.5 cm.
So from the values given:
144π = π* 4.5 * L
4.5L = 144
L = 144/4.5
= 32 cm.
give the line that is parallel to the line y=-5x-2 and goes through (3,-9)
Answer: I don’t think there is such a line. A Line that passes through the point (3,-9) must have a positive slope, unlike the line y=-5x-2, which has a negative slope. If a line where to go through (3,-9), is would intersect the line you presented.
Construct a confidence interval of the population proportion at the given level of confidence. X=540
The lower bound of the confidence interval is 0.55.
What is the confidence interval of the population proportion?A confidence interval for a proportion is a range of values that is likely to contain a population proportion with a certain level of confidence.
Construct a confidence interval of the population proportion at the given level of confidence x equals = 540, n equals = 900, 96% confidence.
The value of p is;
[tex]\rm p=\dfrac{x}{n}\\\\p =\dfrac{540}{900}\\\\p=0.6[/tex]
The standard error of the proportion is:
[tex]\rm \sigma_p=\sqrt{\dfrac{p(1-p)}{n}} \\\\ \sigma_p=\sqrt{\dfrac{0.6(1-0.6)}{540}} \\\\ \sigma_p=\sqrt{\dfrac{0.6\times 0.4}{540}} \\\\ \sigma_p=\sqrt{\dfrac{0.24}{540}} \\\\ \sigma_p=\sqrt{0.00044}\\\\ \sigma_p=0.02[/tex]
The critical z-value for a 94% confidence interval is z = 2.04
The margin of error (MOE) can be calculated as:
[tex]\rm Margin \ of \ error=\sigma_p \times z =2.04 \times0.02 =0.04[/tex]
Then, the lower bound of the confidence interval is;
[tex]Lower \ bound =p-x\times \sigma_p=0.6-0.04=0.55[/tex]
Hence, the lower bound of the confidence interval is 0.55.
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What is the following quotient? startfraction rootindex 3 startroot 60 endroot over rootindex 3 startroot 20 endroot endfraction rootindex 3 startroot 3 endroot 3 2 (rootindex 3 startroot 5 endroot) 40
The value of the quotient expression [tex]\sqrt[3]{60} \div \sqrt[3]{20}[/tex] is [tex]\sqrt[3]{3}[/tex]
What is quotient?The quotient of numbers or expressions is the division of a number or expression by another
How to determine the quotient?The quotient expression is given as:
[tex]\sqrt[3]{60} \div \sqrt[3]{20}[/tex]
Write as a single expression by applying the law of indices
[tex]\sqrt[3]{60 \div 20}[/tex]
Divide 60 by 20
[tex]\sqrt[3]{3}[/tex]
Hence, the value of the quotient expression [tex]\sqrt[3]{60} \div \sqrt[3]{20}[/tex] is [tex]\sqrt[3]{3}[/tex]
Read more about quotient at:
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Answer:
A
Step-by-step explanation:
Endgenuity 2022
Write the first trigonometric expression in terms of the second expression. Cot(x); sin(x)
The first trigonometric expression cot x and sin x in terms of the second expression is one over tan x and one over cosec x.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
Write the first trigonometric expression in terms of the second expression.
The cotangent can be written as
[tex]\cot x= \dfrac{1}{\tan x}[/tex]
And the sine can be written as
[tex]\sin x = \dfrac{1}{\csc x}[/tex]
More about the trigonometry link is given below.
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Find the sum of the geometric series 100+20+…+0.16
Answer:
c) 124.96
Step-by-step explanation:
Geometric series: 100 + 20 + ... + 0.16
First we need to find which term 0.16 is.
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
To find the common ratio r, divide one term by the previous term:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{20}{100}=0.2[/tex]
Therefore, [tex]a_n=100(0.2)^{n-1}[/tex]
Substitute [tex]a_n=0.16[/tex] into the equation and solve for n:
[tex]\implies 100(0.2)^{n-1}=0.16[/tex]
[tex]\implies (0.2)^{n-1}=0.0016[/tex]
[tex]\implies \ln(0.2)^{n-1}=\ln0.0016[/tex]
[tex]\implies (n-1)\ln(0.2)=\ln0.0016[/tex]
[tex]\implies n-1=\dfrac{\ln0.0016}{\ln(0.2)}[/tex]
[tex]\implies n=\dfrac{\ln0.0016}{\ln(0.2)}+1[/tex]
[tex]\implies n=5[/tex]
Therefore, we need to find the sum of the first 5 terms.
Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Therefore, sum of the first 5 terms:
[tex]\implies S_5=\dfrac{100(1-0.2^5)}{1-0.2}[/tex]
[tex]\implies S_5=124.96[/tex]
3 3/4 × 2 10/11? please help
Answer:
3 3/4 x 2 10/11 = 120/11 which is equal to 10 10/11 which is the simplified answer
Step-by-step explanation:
make them inproper so you have 15/4 and 32/11 which the product is 120/11 which you can make a proper fraction which is 10 10/11
16) Consider the sequence of steps to solve the equation:
5(x - 3) =
2
7x
-
Step 1 => 10(x - 3) = 7x
Step 2 = 10x - 30 - 7x
Step 3 => 3x - 30 - 0
Step 4 => 3x = 30
Step 5 => x= 10
Identify the property of equality which gets us from Step 3 to Step 4.
A) Division Property
B) Addition Property
C) Subtraction Property
D) Multiplication Property
Answer:
B) addition property
Step-by-step explanation:
thinking that 3x - 30 - 0 should equal 0.
3x - 30 - 0 = 0
to get rid of numbers on side with variables, we have to add them to both sides (to make it 0 in side with variable.)
3x - 30 - 0 = 0
+30 +0 = +30 +0
3x = 30 <- step 4
Identify the function that best model is the given data
Answer:
f(x) ≈ −2.42x3 + 15.89x2 − 7.55x + 12
Step-by-step explanation:
Notice that the year data are evenly spaced. Check the first differences between the total number or units to see if the data set is linear.
First Differences
41 − 18 = 23
67 − 41 = 26
82 − 67 = 15
69 − 82 = −13
17 − 69 = −52
Because the first differences are not constant, a linear model is not the best model of the data. Check the second differences to see if the data set can be modeled by a quadratic function.
Second Differences
26 − 23 = 3
15 − 26 = −11
−13 − 15 = −28
−52 − (−13) = −39
Because the second differences of the independent variable are not constant, a quadratic model is not the best model of the data. Check the third differences to see if the data set can be modeled by a cubic function.
Third Differences
−11 − 3 = −14
−28 − (−11) = −17
−39 − (−28) = −11
The third differences are approximately the same so we will use a cubic function to represent the data.
Enter the data into a calculator. Plot the data and find the cubic regression equation that best models the data.
f(x) ≈ −2.42x3 + 15.89x2 − 7.55x + 12
Find the Surface Area of the Cone
Answer:
1130,97
Step-by-step explanation:
Find the probability of each event
A bag contains nine real diamonds and
three fake diamonds. If nine diamonds are
picked from the bag at random, what is the
probability that all of them are real?
Answer: If replaced: 0.075 or 7.5%
If not replaced: 0.00455 or 0.455%
Step-by-step explanation:
If the diamonds are replaced after each draw:
The probability of drawing a real diamond is 9/12, found by making the numerator the number of real diamonds and adding the total number of diamonds to find the denominator. 3+9 = 12.
9/12 can be reduced to 3/4 by dividing the numerator and denominator by 3.
To find the probability of all 9 diamonds drawn being real, multiply 3/4 by itself 9 times. [tex]3^9[/tex] = 19683. [tex]4^9[/tex] = 262144. This creates a probability of 19683/262144. This cannot be reduced because there is no common factor. To express as a decimal, divide. 19683/262144 = 0.07508. To turn this into a percent, multiply by 100. 0.07508*100 = 7.508
If the diamonds are not replaced after each draw:
Start with the probability of drawing a single diamond: 9/12. After each draw, both the numerator and denominator have 1 subtracted from them, since there is 1 less real diamond and 1 less diamond in total. This will give you the equation (9/12)*(8/11)*(7/10)*(6/9)*(5/8)*(4/7)*(3/6)*(2/5)*(1/4). This equals 0.00455. To find as a percent, multiply by 100. 0.00455*100 = 0.455
Nolan is designing a new board game, and is trying to figure out all the possible outcomes . How many different possible outcomes are there is he flips a coin, spin a spinner with 5 equal -sized sections labeled Monday ,Tuesday, Wednesday, Thursday, Friday and spins a spinner with three equal sized sections labeled walk , run stop?
Answer:
1 out of 10 i think
Step-by-step explanation
2 sides of a coin + 5 days + 3 movements = 10 outcomes?
one of the terms in the binomial (b+Tv)^n is 3075072b^5v^10. What are the values of T and n?
Answer:
T is 5 and n is 10
Step-by-step explanation:
just relate the (b+Tv)^n with 3075072b^5v^10
6. What is the circumference of the given circle in terms of m?
Answer:
The answer is 24π because r=12
and c=2πr
=2×π×12
=24π
HELPPP MEEEE MATH 7TH PLS PSLSPLS PLS
A: Yes, the sum of two sides are greater than the third side.
B: Yes, the sum of two sides are greater than the third side. (Would be an equiilateral triangl.)
C: No, the sum of two sides are less than the third side.
In general, To determine if 3 side lengths are a triangle, use the triangle inequality theorem, which states that the sum of 2 sides of a triangle must be greater than the third side. Therefore, all you have to do is add together each combination of 2 sides to see if it's greater than the third side.
What is the equation of the line in slope- intercept form
A: y= x+8
B: y=x-8
C: y= 8x+8
D: y=8x-8
Answer:
D
Step-by-step explanation:
Consider ΔWXY and ΔBCD with ∠X ≅∠C, WX ≅ BC, and WY ≅ BD.
Can it be concluded that ΔWXY ≅ ΔBCD by SAS? Why or why not?
no, because the third corresponding sides must also be given as congruent
no, because the corresponding congruent angles listed are not the included angles
no, because all corresponding angles must be given as congruent
yes, because two corresponding sides and a corresponding angle are congruent
Answer: no, because the corresponding congruent angles listed are not the included angles
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Did it on Edge
The hypotenuse of a right triangle measures 19m on leg measures 15m what is the measure of the other leg
Answer:
≈ 11.7 m
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let x be the measure of the second leg , then
x² + 15² = 19²
x² + 225 = 361 ( subtract 225 from both sides )
x² = 136 ( take square root of both sides )
x = [tex]\sqrt{136}[/tex] ≈ 11.7 m ( to the nearest tenth )
Use the quadratic formula to solve for X.
2x- + 6x= -3
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Answer:
x = 0.75 and or x = -0.38
Step-by-step explanation:
If the minus sign after the x was on purpose or if you accidentally put the addition sign after the minus or the other way around basically I have no idea if the solution I provided is correct so here's the solution to both possible equations you might have meant to type instead (and if this was intentional then awesome):
1. 2x - 6x = -3 and 2. 2x + 6x = -3
Let's do 1. first!
[tex]2x-6x=-3[/tex]
Simplify 2x-6x to -4x
[tex]-4x=-3[/tex]
Divide each side by -4
[tex]x=\frac{-3}{-4}[/tex]
And as you know, two negatives equal/make a positive
[tex]x=\frac{3}{4}[/tex] or [tex]x=0.75[/tex]
Now! Let's solve for 2.
[tex]2x+6x=-3[/tex]
Simplify 2x+6x to 8x
[tex]8x=-3\\[/tex]
Divide both sides by 8
[tex]x=\frac{-3}{8}[/tex]
[tex]x=-\frac{3}{8}[/tex] or [tex]x=-0.375[/tex]
PLEASE HELP ME! CAN YOU PLEASE SOLVE!
Answer:
-6
Step-by-step explanation:
-15from both sides then divide the -24 from the left by 4 because you only need one x and your answer is x=-6
