Answer:
83 liters
Step-by-step explanation:
If we call the amount of liters of the 8% iodine solution by x and the amount of liters of the 44% iodine solution by y, we can write the following equations:
x + y = 200
x*0.08 + y*0.44 = 200*0.29
From the first equation, we have that y = 200 - x
Using this value of y in the second equation, we have that:
0.08x + (200 - x)*0.44 = 58
0.08x + 88 - 0.44x = 58
0.36x = 30
x = 30/0.36 = 83.3333 liters
Rounding to nearest liter, we have x = 83 liters
Find m<_6 if m<_8 = 119 degrees.
Angle 6 and angle 8 are corresponding angles, because they are in the same position, but on different parallel lines. Corresponding angles are congruent. So, if the measure of angle 8 is 119 degrees, then the measure of angle 6 is 119 degrees.
Hope this helps! :)
In ΔNOP, the measure of ∠P=90°, the measure of ∠N=15°, and PN = 18 feet. Find the length of OP to the nearest tenth of a foot.
Answer:
4.8
Step-by-step explanation:
The equation below describes a parabola. If a is negative, which way does the
parabola open?
y= ax?
A. Right
B. Left
C. Up
D. Down
The parabola y= ax² opens to the left.
What is Parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
We have the parabolic equation: y= ax²
1. If 'a' is positive, the parabola will open to the right or upwards.
2. If "a" is negative, the parabola opens to the left or downward.
3. The parabola expands either upwards or downwards if x is squared.
4. The parabola opens to the left or right if y is squared.
Now, as we are given the parabola having x² and 'a' is negative.
Thus, from the points 4 and 2, we get,
The given parabola opens to the left.
Learn more about Parabola here:
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a concrete pillar has the shape of a cylinder. it has a diameter of 6 meters and a height of 7 meters. concrete cost $116 per cubic meter how much did the concrete cost for the pillar
Answer:
The cost of the pillar is $22,947.12
Step-by-step explanation:
Diameter of the pillar = 6m
Radius = diameter / 2 = 6 / 2 = 3m
Height if the pillar = 7m
Volume of the pillar = πr²h
π = 3.14
V = 3.14 × 3² × 7
V = 3.14 × 9 × 7
V = 197.82m³
Volume of the pillar is 197.82m³
If 1m³ = $116
197.82m³ will cost $x
X = (197.82 × 116) / 1
X = $22,947.12
The cost of the pillar is $22,947.12
The front face of a cube has side lengths of 15 feet. It is related to the face of a larger cube by a scale factor of 1.8. What are the side lengths of the larger cube?
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Which of the following shows extraneous solutions to the logarithmic equation? (See picture)
Answer:
Option 3
Step-by-step explanation:
log4(x) + log4(x - 3) = log4(-7x + 21)
log4(x² - 3x) = log4(-7x + 21)
x² - 3x = -7x + 21
x² + 4x - 21 = 0
x² + 7x - 3x - 21 = 0
x(x + 7) - 3(x + 7) =0
(x + 7)(x - 3) = 0
x = -7, 3
-7 and 3, both are e extraneous solutions because logs of non-positive numbers don't exist
At x = 3,
-7x + 21 = 0
Triangle ABC is rotated clockwise to create triangle A'B'C'. What is the angle of rotation?
Now
BA 1
5
4 3
2
1
1 2
3
4
5
Answer: 90 degrees
Step-by-step explanation:
The angle of rotation is 90° clockwise rotation
How to determine the angle of rotation?
The coordinates are given as:
A(-2, -2) to A'(-2, 2)
Remove the points
(-2, -2) to (-2, 2)
Replace the coordinates with x and y
(x, y) to (y, -x)
The above represents a 90° clockwise rotation
Hence, the angle of rotation is 90° clockwise rotation
Read more about rotation at:
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Sam volunteers at an animal shelter. He created a line plot to show the weights in pounds of the kittens at the
shelter
Weights of Kittens in Shelter
Pounds
What is the total weight of the kittens in the shelter? Enter your answer in the box
pounds
Answer:
5 pounds
Step-by-step explanation:
The line plot shows that we have 3 kittens with 1/2 pounds, 2 kittens with 1 pound and 1 kitten with 1 1/2 pound.
So, to find the total weight of the kittens in the shelter, we can multiply the number of kittens by their weights, and then sum then all:
Total weight = 3 * (1/2) + 2 * 1 + 1 * (1 + 1/2)
Total weight = 3/2 + 2 + 3/2 = (3 + 4 + 3)/2 = 10/2 = 5 pounds
A lawn darts team has choice of hitting a short field bonus throw or long zone bonus.
1 point is for the short field hit and getting the ball in the long zone is worth 2 points.
The coach tracked the statistics of using attempt strategies.
Short Field (1 point) = 85.8% Long Field (2 points) = 64.2%
If the team gets 10 chances to score this season, which strategy would result in statistically the most points?
Question 1 options:
Short Field
Long Field
Answer: i believe it is short field
Answer:
B. Long Field
Step-by-step explanation:
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Divide.
1/8 ÷ 9
Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:
1/72
Step-by-step explanation:
Answer:
1/72
Step-by-step explanation:
1/8 divided by 9 = 1/8 times 1/9.
We have ti flip 9/1 so we get 1/9
You multiply 9 by 8 you get 72
so the answer is 1/72
Brian invests £1300 into his bank account.
He receives 10% per year simple interest.
How much will Brian have after 3 years?
Give your answer to the nearest penny where appropriate.
Answer:
£1690
Step-by-step explanation:
Amount invested by Brian = £1300
rate of simple interest = 10%
To find money Brian will have after three years
He will have amount invested in bank and interest earned in three years from that amount.
Simple interest for any principal amount p is given by
SI = P*R * T /100
where SI is simple interest earned
T is time period for which simple interest is earned
R is rate of interest
Substituting value of P , R and T we have
SI = 1300*10* 3 /100 = 390
Therefor interest earned will be £390
Total money with Brian after three years = principal amount invested + interest earned in 3 years
= £1300 + £390 = £1690
Janice has car insurance that she must pay four times a year. If each payment is $156, how much money should she set aside each month to
cover her car insurance?
OA $13
OB. $26
oc $39
OD. $52
Answer:
C
i hope this helped you
Answer:
D
Step-by-step explanation:
cause if you pay 4 times a year that means you set money aside every three months which means that you set 52 dollars every month
Trina and Seth walk 3 miles south and 5 miles east to get from their canoe to their tent. If a walkway existed between the canoe and tent, how far would they then haveto walk? Round to the nearest mile. (PLEASE SHOW WORK!)
Answer:
A. 6
Step-by-step explanation:
[tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]
[tex]3^{2}[/tex]+[tex]5^{2}[/tex]=[tex]c^{2}[/tex]
[tex]3^{2}[/tex]=9
[tex]5^{2}[/tex]=25
25+9=34
[tex]\sqrt{34}[/tex]= 5.83
Round it and its 6
A game room has a floor that is 120 feet by 75 feet. A scale drawing of the floor on grid paper uses a scale of 1 cm: 5 feet.
What are the dimensions of the scale drawing?
Answer:
24cm x 15cm
Step-by-step explanation:
120/5 = 24 cm
as 24 cm x 5 = 120 feet.
We check 75 feet
75/5 = 15 cm
as 15 cm x 5 = 75 feet
So the answer is 24cm x 15cm
Where would 4 cups be placed on the number line
Answer:
D
Step-by-step explanation:
There are 2 cups in a pint, so 3 cups would be 1.5 pints. :)
-5x+2=22
A. 96
B. 6
C. 4
D. -4
O need the answer
The head-to-tail length of a species of fish is normally distributed, with a
mean of 17.4 cm and a standard deviation of 3.2 cm. One fish is 16.3 cm
long. What is the score of the length of this fish? Round your answer to two
decimal places.
A. 0.54
B. 0.34
C. -0.34
D. -0.54
Answer:
C. -0.34
Step-by-step explanation:
We have that for a normal distribution, the value of z can be calculated using the following formula:
z = (x - m) / sd
where x is the value to evaluate, m the mean and sd the standard deviation, we have those values x = 16.3, m = 17.4 and sd = 3.2
if we replace we have:
z = (16.3 - 17.4) /3.2
z = -0.3437
if we round to 2 decimal places, it would be -0.34, that is, the answer is C.
The z-score for a fish measuring 16.3 cm, with a mean length of 17.4 cm and a standard deviation of 3.2 cm, is -0.34.
The score of the length of the fish, also known as the z-score, is calculated by subtracting the mean from the observed value and then dividing by the standard deviation. Using the provided data, we have a mean (μ) of 17.4 cm and a standard deviation (σ) of 3.2 cm. The fish in question measures 16.3 cm.
To find the z-score, the calculation is as follows:
Z = (X - μ) / σ
Z = (16.3 cm - 17.4 cm) / 3.2 cm
Z = -1.1 cm / 3.2 cm
Z = -0.34 (rounded to two decimal places)
Therefore, the z-score for a fish that is 16.3 cm long is -0.34, which corresponds with answer option C.
You roll a number cube 20 times. The number 4 is ro
probability of rolling a 4?
O 40%
O 25%
O 20%
0 17%
A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h,
in feet after t seconds is given by the function h=-167 + 120t + 10. How long does it take to
reach maximum height? What is the boulder's maximum height? Round to the nearest
hundredth, if necessary.
a. Reaches a maximum height of 235.00 feet in 3.75 seconds.
b. Reaches a maximum height of 10.00 feet in 7.50 seconds.
c. Reaches a maximum height of 7.58 feet in 3.75 seconds.
d. Reaches a maximum height of 15.16 feet in 7.5 seconds.
Answer:
Reaches a maximum height of 235.00 feet in 3.75 seconds.
Step-by-step explanation:
The height of the boulder, h, in feet after t seconds is given by the function is given by :
[tex]h=-16t^2+120t+10[/tex] .....(1)
For maximum height, put [tex]\dfrac{dh}{dt}=0[/tex]
i.e.
[tex]\dfrac{d(-16t^2+120t+10)}{dt}=0\\\\-32t+120=0\\\\32t=120\\\\t=3.75\ s[/tex]
Put t = 3.75 in equation (1). So,
[tex]h=-16(3.75)^2+120(3.75)+10\\\\h=235\ \text{feet}[/tex]
So, the boulder's maximum height is 235 feets and it takes 3.75 s to reach to its maximum height.
Simplify 4^5/4^3 and show steps
Answer:
16
Step-by-step explanation:
4^5/4^3
4^5-3
4^2
16
Hope this helps :)
Plz plz plz plzplzplzplz help me plz plz help plz plz show me plz plz thx plz
Answer: 97
Step-by-step explanation:
4,074 / 42
hope this helped
IM TAKING AN EXAM AND I NEED SO MUCH HELP!!
Show how to find the inverse of f(x) = x^3 - 5. Calculate 3 points on f(x) and use these points to show that the inverse is correct.
Answer:
[tex]f^{-1}(x) = \sqrt[3]{x+5}[/tex]
Step-by-step explanation:
A function [tex]f^{-1}[/tex] is the inverse of f if whenever y =f(x) and [tex]x =f^{-1}[/tex]
To find the inverse of f(x) = [tex]x^{3}[/tex] - 5, we use the following steps:
Step 1 : Put y for f(x) and solve for xy = [tex]x^{3}[/tex] - 5
<=> [tex]x^{3}[/tex] = y + 5
<=> x = [tex]\sqrt[3]{y+ 5}[/tex]
Step 2: Put [tex]f^{-1}(y)[/tex] for x, we have:[tex]f^{-1}(y) =\sqrt[3]{y+5}[/tex]
Step 3: Interchange y =x, we have[tex]f^{-1}(x) = \sqrt[3]{x+5}[/tex]
Let Calculate 3 points on f(x)
x = 0 => y = -5
x = 1 => y = -4
x = 2 => y = 3
Let Calculate 3 points on [tex]f^{-1}[/tex] (x)
x = -5 => y = 0
x = -4 => y = 1
x = 3 => y = 2
Yes, the inverse is correct because:
the domain of the inverse function is the range of the original function the range of the inverse function is the domain of the original functionHelp please...........................
Answer: n=3, hope this helps! c:
The vertex of the parabola below is at the point (5,-3). Which of the equations
below could be the one for this parabola?
M
10-1
MC
10
(5.-3)
10
A. X = 3(y + 3)2 + 5
B. x = 3(y - 5)2 - 3
C. X= -3(y + 3)2 + 5
D. y = -3(x - 5)2-3
The vertex of a parabola is written as (h,k) so h = 5 and k = -3.
H is subtracted from x inside parentheses and k is added at the end of the equation.
The equation is also written as y =
The answer should be D.
Answer c also works, so there are two correct answers.
the radius of a circle is 5 inches what is the area of a sector biunded by 180 degrees arc
The area of a sector with a radius of 5 inches and a 180-degree arc is half the area of the full circle, resulting in 39.27 square inches when rounded.
Explanation:The area of a sector of a circle with radius 5 inches that is bounded by a 180-degree arc can be found by first calculating the area of the entire circle and then taking half of that area, since 180 degrees is half of the full 360 degrees of a circle. The formula to calculate the area of a circle is A = πr². For a radius (r) of 5 inches, the entire circle's area would be A = π(5 inches)².
Thus, the entire circle area is A = 3.1415927 × (5 inches)² = 78.53981633974483 square inches. Since the sector is half of the circle, the area of the sector would be 39.269908169872415 square inches, or when rounded to two decimal places, 39.27 square inches.
What is the value of x in the equation below? –13 –9 3 7
Answer:
7
Step-by-step explanation:
It just is
A photo is printed on a 20-inch by 24-inch piece of paper. The photo covers 320 square inches and has a ubiform border. What is the width of
the border?
Answer:2 in.
Step-by-step explanation:
Given
Dimension of photo frame is [tex]20\ in.\times 24\ in.[/tex]
If the photo cover an area of [tex]320\ in.^2[/tex]
Suppose x be the width of border
Therefore dimension of frame without border is
[tex]A'=(20-2x)(24-2x)[/tex]
And [tex]A'[/tex] must be equal to [tex]320\ in.^2[/tex]
So,
[tex]\Rightarrow (20-2x)(24-2x)=320[/tex]
[tex]\Rightarrow (10-x)(12-x)=80[/tex]
[tex]\Rightarrow 120-10x-12x+x^2=80[/tex]
[tex]\Rightarrow x^2-22x+40=0[/tex]
[tex]\Rightarrow x^2-20x-2x+40=0[/tex]
[tex]\Rightarrow (x-2)(x-20)=0[/tex]
Thus there are two values of x out of which [tex]x=20\ in.[/tex] is not valid because it is not feasible
thus width of border is [tex]x=2\ in.[/tex]
What are the solutions of x2 -7x+13 = 0 ?
Answer:
x =(7-√-3)/2=(7-i√ 3 )/2= 3.5000-0.8660i
x =(7+√-3)/2=(7+i√ 3 )/2= 3.5000+0.8660i
Step-by-step explanation:
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-7x+13
The first term is, x2 its coefficient is 1 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is +13
Step-1 : Multiply the coefficient of the first term by the constant 1 • 13 = 13
Step-2 : Find two factors of 13 whose sum equals the coefficient of the middle term, which is -7 .
-13 + -1 = -14
-1 + -13 = -14
1 + 13 = 14
13 + 1 = 14
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 7x + 13 = 0
This may be a lot sorry it is confusing if it is wrong i'm so sorry don't come at me wrong please!
Which is the graph of y=2/(x+1)-6
Answer:
A on EDGE2020
The graph of the rectangular hyperbola that has the equation of the horizontal asymptote of y = -6 and the vertical asymptote of x = -1 will be drawn below.
What is the rectangular hyperbola?The asymptotes or axes of a rectangular hyperbola are parallel to one another. The conjugate axis and transverse axes have lengths that are identical.
An asymptote is a line that constantly reaches a given curve but does not touch at an infinite distance.
The rectangular hyperbola is shifted below. Then the horizontal also gets shifted below by 6 units. Then the equation of the horizontal asymptote is given as,
y = - 6
Then the equation of the vertical asymptote is given as,
x + 1 = 0
x = - 1
The graph of the rectangular hyperbola that has the equation of the horizontal asymptote of y = -6 and the vertical asymptote of x = -1 will be drawn below.
More about the rectangular hyperbola link is given below.
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evaluate the expression for q=8.
7q
q=8
soo
7(8)=64
64 is the final answer.