It will take them 30 minutes
The faster computer will take approximately 22.5 minutes to do the job on its own.
Explanation:Let's assume that the faster computer can complete the job on its own in x minutes.
If the slower computer takes 45 minutes to complete the job on its own, it means that in 1 minute it completes 1/45th of the job.
Working together, the two computers can complete the entire job in 15 minutes. So in 1 minute, they can complete 1/15th of the job.
Therefore, 1/45 + 1/x = 1/15
Simplifying the equation, we get 1/x = 1/15 - 1/45
Substituting the numerator values with a common denominator, 1/x = (3/45) - (1/45) = 2/45
Now, solving for x, we get x = 45/2 = 22.5
So, it will take the faster computer approximately 22.5 minutes to do the job on its own.
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What is the exact value of sin 60° ?
Enter your answer, as a simplified fraction, in the box.
$$
Answer:
The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].
Step-by-step explanation:
Recall that [tex]\sin(60\degree)[/tex] is a special angle that can be obtained using an equilateral triangle.
The right triangle obtained using one of the lines symmetry was used to find the exact value of [tex]\sin(60\degree)[/tex] using SOH-CAH-TOA
The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].
PLEASE HELP!!!!!! HURRY PLEASE!
You are going to create a circle graph to represent some data. How many degrees should a section representing 65 out of a hundred be?
A. 234°
B. 65°
C. 100°
D. 13°
Answer: OPTION A.
Step-by-step explanation:
We know that a circle measures 360 degrees. Then, to determine the size of a section, we need to multiply the percent of the category by 360 degrees.
First, we need to write 65 out of a hundred in decimal form:
[tex]\frac{65}{100}=0.65[/tex]
Now, let be "x" the degrees of the section representing 65 out of a hundred. We need to multiply 360 degrees by 0.65. Therefore, we get this result:
[tex]x=360\°*0.65\\x=234\°[/tex]
This matches with the option A.
The degree measurement for a section representing 65 out of 100 on a circle graph is 234 degrees. This is obtained by forming a ratio of the data point to the total data and multiplying by 360 (the total degrees in a circle).
Explanation:To determine the degree measurement for a section on a circle graph, we must understand that a full circle consists of 360 degrees. The proportion that every bit of data takes in that circle is found by making a ratio of the data point to the total data multiplied by 360 degrees. Therefore, to find the proportion of 65 out of 100, we would make a ratio of 65 to 100 and multiply that by 360. Which comes out to: (65/100) * 360 = 234 degrees. So the correct answer would be 234 degrees (Option A).
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If 21 more than 3 times a number is -15 , what is the number?
A: 2
B: -12
C: -2
D: 12
Let X = the number.
You have 21 more than 3 times the number which is:
3x +21 = -15
Subtract 21 from both sides:
3x = -36
Divide both sides by 3:
x = -36 /3
x = -12
The answer is B.
Answer:
-13
Explanation:
Rewrite Equation:
(3 · x) + 21 = -15
Subtract 21 From Both Sides:
(3 · x) + 21 - 21 = -15 - 21
Simplify:
3x = -36
Divide Both Sides By 3:
[tex]\bold{\frac{3x}{3} \ = \ \frac{-36}{3} }[/tex]
Simplify:
x = -12
Mordancy.
A tree outside Ellie's house casts a 125-foot shadow. At the same time of the day, Ellie casts a 5.5-foot shadow. If Ellie is 4 feet 10 inches tall, how tall is the tree in feet?
Answer:
The tall of the tree is about 109.85 feet
Step-by-step explanation:
* Lets study the situation in the problem
- The tree and its shadow formed a right angle triangle with legs
x the tall of the tree and 125 feet the shadow of the tree
- Ellie and her shadow formed a right triangle with legs 4 feet and
10 inches the tall of Ellie and 5.5 feet the shadow of Ellie
- The two triangles are similar
- There is an equal ratio between the corresponding sides of the
similar triangles
# Ex: If triangles ABC and XYZ are similar
∴ AB/XY = BC/YZ = AC/XZ
* Lets use this rule to solve the problem
∵ The tall of the tree is x
∵ The tall of Ellie is 4 feet and 10 inches
- Lets change the tall of Ellie to feet only
∵ 1 foot = 12 inches
∴ 10 inches = 10/12 = 5/6 foot
∴ The tall of Ellie is 4 feet and 5/6 foot = 4 + 5/6 = 29/6 feet
∵ The shadow of the tree is 125 feet
∵ The shadow of Ellie is 5.5 feet
- By using similarity ratio
∴ Tall of tree/tall of Ellie = shadow of tree/shadow of Ellie
∴ x/(29/6) = 125/5.5 ⇒ using cross multiplication
∴ 5.5(x) = 125(29/6) ⇒ divide both sides by 5.5
∴ x ≅ 109.85 feet
* The tall of the tree is about 109.85 feet
Answer:
The tall tree is about 109.85
Step-by-step explanation:
Hope this helps!
Pam drove her car 288 miles using a total of 12 gallons. How many gallons would it take for her to drive a total of 156 miles? Gallons
Answer:
6.5 Gallons
Step-by-step explanation:
288 miles / 12 gallons = 24 mpg
156 miles / 24 mpg = 6.5 gallons
The sum of two numbers is 11, and their difference is 9. What are the two numbers?
Answer:
10 and 1
Step-by-step explanation:
Let x and y represent the two numbers. The problem statement lets us write two equations describing their relationships:
x + y = 11
x - y = 9
Adding these equations together, we have ...
(x +y) +(x -y) = (11) +(9)
2x = 20
x = 10 . . . . . . . . . you will notice this is the average of the two given numbers
Then ...
10 + y = 11 . . . . substitute for x in the first equation
y = 1 . . . . . . . subtract 10
The two numbers are 10 and 1.
Sarah saw a hammer that was $3.50 more than twice the cost of a screwdriver. The hammer was $15.50. What was the cost of the screwdriver?
Answer:
$6
Step-by-step explanation:
$15.50 is $3.50 more than $12. And $12 is twice $6. The cost of the screwdriver is $6.
PLEASE HELP ME! PLEASE!!
Which scale factors produce an expansion under a dilation of he original image?
Choose all answers that are correct.
a)-0.75
b)-2
c)0.75
d)2
Which scale factors produce a contraction under a dilation of he original image?
Choose all answers that are correct.
a)-1.8
b)-0.8
c)1.8
d)0.8
Answer:
1. 0.75
2. -0.8
mark me brainlyest
First when looking at dialations, ignore the negative signs. They do not affect the expansion or contraction.
An expansion is any number greater than 1 and a contraction is any number less than 1.
Expansion: b) -2 and d) 2
Contraction: b) - 0.8 and d) 0.8
Over the summer, for every 14 Okra seeds Dana planted, 9 plants grew. If he planted 182 seeds how many grew into plants
Answer:
117
Step-by-step explanation:
182/14=13
13x9=117
The volumes of two similar solids are 1728 m³ in 343 m³. The surface area of the larger solid is 576 m². What is the surface area of the smaller solid
A. 196 m²
B. 76 m2
C. 1372 m²
D. 392 m²
Answer:
A. 196 m²
Step-by-step explanation:
The two similar solids have volumes 1728 m³ and 343 m³.
The ratio of their side lengths is :
[tex]\sqrt[3]{1728}:\sqrt[3]{343}[/tex]
This simplifies to:
[tex]12:7[/tex]
If the surface area of the larger solid is 576 m², then the surface area of the smaller solid is given by:
[tex]\frac{7^2}{12^2}\times 576=196[/tex]
The correct answer is A
what is the distance between the points (-4, 2) and (1, -3) on the coordinate plane?
A. 7.07 units
B. 2.83 units
C. 5.83 units
D. 7.21 units
Answer:
A. 7.07 units
Step-by-step explanation:
Use the distance formula for coordinates:
[tex]d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2 }[/tex]
Fill in the coordinates accordingly:
[tex]d=\sqrt{(1-(-4))^2+(-3-2)^2}[/tex]
which simplifies down to
[tex]d=\sqrt{25+25}[/tex]
which is of course
[tex]d=\sqrt{50}[/tex]
Plug that into your calculator and you'll get the answer
Cherry is paid $72.00 for working six hours in a library. If the amount paid is proportional to the number of hours worked, what is the constant of proportionality?
Answer:
She's being paid six hours per hour
Step-by-step explanation:
She's being paid six hours per hour
72/6 = 6
help please with this question
Let f(x)=x^2-6x-27. enter the x-intercepts of the quadratic function in the boxes.
Step-by-step explanation:
0 = x² - 6x - 27
a = 1, b = -6, c = -27 Factor using AC method.
ac = (1)(-27) = -27
Factors of -27 that add up to -6 are -9 and 3.
Therefore:
0 = (x - 9) (x + 3)
x = -3, x = 9
The x-intercepts are (-3, 0) and (9, 0).
Solve for x. Round your answer to 2 decimal places.
Answer:
x = 29.91
Step-by-step explanation:
Cos (53) = 18/x
x = 18 / Cos(53)
x = 18/ 0.6018
x = 29.91
For this case we have that by definition of trigonometric relations of a rectangular triangle, that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:
[tex]cos (53) = \frac {18} {x}[/tex]
Clearing x:
[tex]x = \frac {18} {cos (53)}\\x = \frac {18} {0.60181502}\\x = 29,9095226969[/tex]
Rounding:
[tex]x = 29.91[/tex]
Answer:
29.91
1. Two intersecting lines form how many
a. pairs of supplementary angles
b. pairs of complementary angles
c. pairs of adjacent angles
d. linear pairs of angles
e. pairs of verticle angles
This question isn't multiple choice by the way. It asks for each, and I know this may be a bit much to ask but if any of you can find images for each response that'd be great as well. But if not answering is also fine. Thanks!
Answer:
6 pairs of supplementary (when perpendicular)
a pair of complementary(0 for perpendicular)
4 pairs of adjacent
4 pairs of linear
2 pairs of vertical
Please please help me out
Step-by-step explanation:
[tex] { \sin(x) }^{2} + { \cos(x) }^{2} = 1 \\ { \cos(theta) }^{2} = \frac{9}{16} \\ \: { \sin(theta) }^{2} = \frac{6}{16} = \frac{3}{8} \\ \: \sin(theta) = \frac{ \sqrt{3} }{ \sqrt{8} } \\ \sin(theta ) = \frac{ \sqrt{24} }{8}
= \frac{ 2\sqrt{6} }{8} = \frac{ \sqrt{6} }{4}
[/tex]
Answer:
[tex]\frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1, then
sinx = [tex]\sqrt{1-cos^2x}[/tex]
sinΘ = [tex]\sqrt{1-(3/4)^2}[/tex]
= [tex]\sqrt{1-\frac{9}{16} }[/tex] = [tex]\sqrt{\frac{7}{16} }[/tex] = [tex]\frac{\sqrt{7} }{4}[/tex]
The values given in the table below are the coordinates of points on a line.
What is the slope of this line?
Answer:
slope = 5
Step-by-step explanation:
To calculate the slope m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (2, 8) ← ordered pairs from the table
m = [tex]\frac{8-3}{2-1}[/tex] = 5
The slope of a line can be calculated using the formula (y2-y1) / (x2-x1) using any two points on the line. The result you get from this calculation is the slope of the line.
Explanation:To find the slope of a line from a set of coordinates, you need two points from the line. Let's consider these two points as (x1, y1) and (x2, y2). The formula for the slope is (y2-y1) / (x2-x1). This formula shows the change in y-values divided by the change in x-values, often referred to as 'rise over run'.
If, for instance, from your table the two points are (3,4) and (5,8), substitute these values into the formula: Slope = (8-4) / (5-3) = 4/2 = 2. So the slope of the line is 2.
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Find the values of m and b that make the following function differentiable.
f(x) = {x^2, x less than or equal to 2
mx+b, x>2}
thank you so much!!
Both x² and mx + b are differentiable functions of x (they are both polynomials), so if f(x) is also differentiable, we need to pay special attention at x = 2 where the two pieces of f meet.
Continuity means that the limit
[tex]\displaystyle \lim_{x\to2} f(x)[/tex]
must exist.
From the left side, we have x < 2 and f(x) = x², so
[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} x^2 = 4[/tex]
From the right, we have x > 2 and f(x) = mx + b, so
[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (mx+b) = 4m+b[/tex]
It follows that 4m + b = 4.
Differentiability means that the limit
[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2}[/tex]
must exist.
From the left side, we again have x < 2 and f(x) = x². Then
[tex]\displaystyle \lim_{x\to2^-}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{x^2-4}{x-2} = \lim_{x\to2} (x+2) = 4[/tex]
From the right side side, we have x > 2 so f(x) = mx + b. Then
[tex]\displaystyle \lim_{x\to2^+}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{(mx+b)-(2m+b)}{x-2} = \lim_{x\to2} \frac{mx-2m}{x-2} = \lim_{x\to2}m = m[/tex]
The one-sided limits must be equal, so m = 4, and from the other constraint it follows that 16 + b = 4, or b = -12.
Flipping through a magazine, Hiccup sees an advertisement for Toothless Toothpaste. The ad says that it is recommended by 4 out of 7 dragons dentists. toothless If 1,500 dragon dentists were surveyed, about how many would recommend Toothless Toothpaste? Explain your reasoning!
Answer:
375
Step-by-step explanation:
So first you would want to divide 1,500 by 4 because the ratio is 4:7. The answer you get if you divide 1,500 by 4 is 375. This is your answer because if you divide 1,500 by 4 you are seeing out of how many 'dentist' would recomend this product.
1500/4
375
Use a calculator
Very helpful
On in-line skates, Bradley skates 4 miles in 20 minutes. At this speed, how long would it take him to skate the entire length of a 12-mile bike path?
Answer:
1 hour (60 minutes)
Step-by-step explanation:
If his speed remains the same, that means that this is a linear relationship. y increases at the same rate as x increases. Direct variation and all of that. Because this is a linear relationship, it can be solved using proportions. Set up the given info in a ratio with miles on the top and minutes on the bottom:
[tex]\frac{miles}{minutes}:\frac{4}{20}[/tex]
Now we want to know how long (unknown number of minutes) it will take him to go 12 miles. Keep miles with miles and minutes with minutes:
[tex]\frac{miles}{minutes}:\frac{4}{20}[/tex]=[tex]\frac{12}{x}[/tex]
We can cross multiply now to get 4x = 12(20) and 4x = 240. That means that x=60. It will take him 60 minutes (1 hour) to go 12 miles.
Answer: 60 minuites
Step-by-step explanation: actully the dude thats on top of me its only 60 mins not 1hr and 60 mins
A parallelogram has vertices (5, 0), (3, -3), (-4, -3), and (-2, 0). What is the approximate perimeter of the parallelogram?
Check the picture below.
so the top and bottom segments are simply 7 units, we can read that off the grid. Let's find the length of the other two segments, "c".
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ c=\sqrt{2^2+3^2}\implies c=\sqrt{13} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of the parallelogram}}{7+7+\sqrt{13}+\sqrt{13}}\qquad \approx \qquad 21.21[/tex]
Answer:
C: 30 units
Step-by-step explanation:
on edge 2021! hope this helps!!~ d=(´▽｀)=b
How do you solve for the quotient of (x^-1) - 1 ÷ x - 1?
[tex]\bf x^{-1}-1\div x-1\implies \implies \cfrac{1}{x}-1\div x-1\implies \cfrac{\frac{1}{x}-1}{~~x-1~~}\implies \cfrac{~~\frac{1-x}{x}~~}{\frac{x-1}{1}} \\\\\\ \cfrac{1-x}{x}\cdot \cfrac{1}{x-1}\implies \cfrac{-(\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix})}{x}\cdot \cfrac{1}{\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies -\cfrac{1}{x}\implies -x^{-1}[/tex]
A porfessional basket court is in the shape of a rectangle it is 50 Feet wide and 94 feet long a player runs on time around the edge of the court how far dose the player run?
Answer:
288 ft.
Step-by-step explanation:
Find the perimeter. 50+50+94+94 = 288
The equation for a circle is x^2 + 10x + y^2 + 12y + 52 = 0
What is the equation of the circle in standard form?
(X+5)^2+(y+6)^2=61 and then to find the radius take the square root of both sides
Koen is training for a track meet. Last month, he ran for four and a half hours. He averaged a speed of six miles per hour. How many miles did Koen run?
Hopefully I read the question right, if not I'm sorry
Koen ran for 4 and a half hours, which is also 4.5 hours
Since he averaged a speed of 6 mph, I multiply the number of hours by speed each hour, which is 4.5*6
4.5*6=27
Koen ran 27 miles.
Answer:
38 miles
Step-by-step explanation:
study island
If he randomly chooses two students, one at a time, what is the probability that they are both girls?
Answer:
B) 15/91
Step-by-step explanation:
Probability of a girl as first choice is ...
number of girls / total number of students = 6/14 = 3/7
Probability of a girl as second choice (given a girl as first choice) is ...
number of girls / remaining number of students = 5/13
Then the probability of the two events is the product of their individual probabilities:
(3/7)·(5/13) = 15/91 . . . . . matches choice B
Which of the following points is a solution to the system of linear inequalities?
{y≤2x-5
y>-3x
A.
(1, 1)
B.
(–2, 2)
C.
(5, 3)
D.
(–4, 4)
Answer:
C. (5, 3)
Step-by-step explanation:
this point is within the answer area... look below at the graph of both linear inequalities
For this case we have the following system of inequations:
[tex]y\leq2x-5\\y> -3x[/tex]
We must replace each of the points and verify that the inequalities are met:
Point A: (1,1)
[tex]1 \leq2 (1) -5\\1 \leq2-5\\1 \leq-3[/tex]
It is not fulfilled!
Point B: (-2,2)
[tex]2 \leq2 (-2) -5\\2 \leq-4-5\\2 \leq-9[/tex]
It is not fulfilled!
Point C: (5,3)
[tex]3 \leq2 (5) -5\\3 \leq10-5\\3 \leq5[/tex]
Is fulfilled!
[tex]3> -3 (5)\\3> -15[/tex]
Is fulfilled!
Point D: (-4,4)
[tex]4 \leq2 (-4) -5\\4 \leq -8-5\\4 \leq -13[/tex]
It is not fulfilled!
Thus, the point that is the solution of inequalities is:
(5,3)
ANswer:
(5,3)
Please help me out please
Answer:
48 ft³
Step-by-step explanation:
The volume (V) of the pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × perpendicular height (h)
Calculate h using the right triangle formed by a segment from the vertex to the midpoint of the base and across to the slant face ( the hypotenuse )
Using Pythagoras' identity on the right triangle then
h² + 3² = 5²
h² + 9 = 25 ( subtract 9 from both sides )
h² = 16 ( take the square root of both sides )
h = [tex]\sqrt{16}[/tex] = 4
area of square base = 6² = 36, hence
V = [tex]\frac{1}{3}[/tex] × 36 × 4 = 12 × 4 = 48 ft³
The work of a student to solve a set of equations is shown: Equation A: y = 4 − 2z Equation B: 4y = 2 − 4z Step 1: −4(y) = −4(4 − 2z) [Equation A is multiplied by −4.] 4y = 2 − 4z [Equation B] Step 2: −4y = 4 − 2z [Equation A in Step 1 is simplified.] 4y = 2 − 4z [Equation B] Step 3: 0 = 6 − 6z [Equations in Step 2 are added.] Step 4: 6z = 6 Step 5: z = 1 In which step did the student first make an error? (5 points)
ANSWER
Step 2
EXPLANATION
The system of equations are:
Equation A:
[tex]y = 4 - 2z[/tex]
Equation B:
[tex]4y=2 - 4z[/tex]Step 1: Multiply equation A by -4.
Equation A:
[tex] - 4(y) = - 4(4 - 2z)[/tex]
Equation B:
[tex]4y=2 - 4z[/tex]
Step 2: Simplify equation A in step 1,
Equation A:
[tex] - 4y= - 16 + 8z[/tex]
This is where the student made the first error.
He didn't expand the second parenthesis correctly.
Answer:
The student made the first mistake in step 2.
Step-by-step explanation:
The sum of the digits of a two-digit number is 13. The units digit is one more than twice the tens digit. Find the number, and...
The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit, and the tens digit equals to the sum of the other two. Find the number.
Answer:
1)49
2)231
Step-by-step explanation:
1)
4+9=13
4*2=8
8+1=9
2)
2+3+1=6
2+1=3
1*2=2
Answer:
#1. 49 #2. 231
Step-by-step explanation:
#1. 4 x 2 + 1 =
8 + 1 =
9
add 40 + 9 = 49
#2. x + 2x + (x + 2x) = 6
6x = 6
x = 1
2x = 2
x + 2x = 3
(2 x 100) + (3 x 10) + 1 or 231.
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