The horizontal distance to the nearest hundredth of a meter, that Liola covered is 129.03 m (option A)
How to determine the horizontal distance?The following data were obtained from the question:
Hypotenuse = 130 mAngle (θ) = 7°Horizontal distance = Adjacent =?The horizontal distance Liola covered as she drives 130 m up the hill can be obtained as follow:
Cos θ = Adjacent / Hypotenuse
Cos 7 = Horizontal distance / 130
Cross multiply
Horizontal distance = 130 × Cos 7
= 130 × 0.9925
= 129.03 m
Thus, the horizontal distance Liola covered is 129.03 m (option A)
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A snack-size bag of pretzels contains 0.5 ounce. How many ounces of pretzels come in a bulk pack that contains 64 snack size bags.
[tex]__________________________[/tex]
Given:Each bag of pretzels contain = 0.5 ozAnswer & Solution:64 x 0.5 oz = 32 oz
Therefore, 64 bags of pretzels contains 32 oz of pretzels.
$400 interest is earned on a principal of $2000 at a simple interest rat 5% interest per year.for how many year was the principal invested
Answer:
4 Years.
Step-by-step explanation:
Given:Principle ⇒ 2000
Interest ⇒ 400
Rate ⇒ 5%
To Find:Time ⇒ _
Solution:Simple interest ⇒ p * x * t / 100
⇒ 400 = 2000 * 5 * t / 100
⇒ 400 = 200 * 5 * t / 10
⇒ 400 = 20 * 5 * t
⇒ t = 400 / 20 * 5
⇒ t = 40 / 2 * 5
⇒ t = 20 / 5
⇒ t = 4
The rate at which people learn about a secret is directly proportional to the number of people who know the secret. If two people know the secret on day 0, and 20 people know it on day 2, how long will it take for the whole school (4000 people) to know?
Answer:
between 222 and 223 days
Step-by-step explanation:
This relation includes the point (0, 2).
A proportional relation must include the point (0, 0).
This is not proportional, but it may be linear.
Points: (0, 2), (2, 20)
y = mx + b
20 = (20 - 2)/(2 - 0) × 2 + b
20 = 18/2 × 2 + b
b = 2
y = 18x + 2
When 4000 people know, y = 4000.
y = 18x + 2
4000 = 18x + 2
3998 = 18x
x = 3998/18
x = 222.111...
Answer: between 222 and 223 days
An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage, is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. What are the appropriate hypotheses?
H0: μ = 76.4 versus Ha: μ < 76.4, where μ = the true mean height of all trucks
H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks
H0: μ = 76.4 versus Ha: μ < 77.1, where μ = the true mean height of all trucks
H0: μ = 76.4 versus Ha: μ > 77.1, where μ = the true mean height of all trucks
The Hypotheses are; Null Hypothesis; H₀: μ = 76.4 and Alternative Hypothesis; Hₐ: μ > 76.4 where μ is the true mean height of all trucks.
How to Define Hypotheses?We are given;
Population Mean; μ = 76.4 inches
Sample Mean; x' = 77.1 inches
Sample standard deviation; s = 5.2 inches
Sample size; n = 100 trucks
Now we can thus define the hypotheses as;
Null Hypothesis; H₀: μ = 76.4
Alternative Hypothesis; Hₐ: μ > 76.4
where μ is the true mean height of all trucks
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Find the area of the rectangle or square 19 3 km and 38.4 km.
Answer:
Area of rectangle is 741.12km^2
Area of square is 1474.56km^2
Step-by-step explanation:
Formula for Area of a rectangle= length x breadth
Area = l x b = 19.3 km x 38.4 km (substitute the numbers)
Area = 741 km^2
OR
Area of square = length x length
Area = l x l = 38.4 x 38.4
Area = 1474.56 km^2
Prove that the side lengths 3, 9, and 12 do not represent a right triangle. Make sure to include ALL calculations.
Step-by-step explanation:
a^2+b^2=c^2
3^2+9^2 not equal to 12^2
A stunt plane ended a maneuver
100 meters above the top of a
skyscraper before dropping more
than 12 meters. What is the
highest altitude the plane could be
after the drop?
Answer:
The stunt plane finally finished his stunt at a height of 300m above the skyscraper which means he is at a height of h0 + 300 above sea level
Therefore , the total elevation (e) would be :
e = 300 + 100
= 400m
The equation y=37.8xy=37.8x represents the number of miles, yy, that Julian can drive his car for every xx gallons of gas. Find the rate of change.
The rate of change of Julian given the equation y = 37.8x is 37.8
How to find the rate of changeThe equation:
y = 37.8x
where,
y = number of miles that Julian can drivex = gallons of gas used37.8 = constant = rate of changeIf x = 3 gallons
y = 37.8x
= 37.8 × 3
y = 113.4 miles
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troy organizes a samll party there are 30 glasses of drinks at the party 20 of which contain an orange flavored drink what is the probability that a randomly selected drink will be orange flavored
Answer:
66(2/3) %
Step-by-step explanation:
There are 30 possible outcomes because there are 30 cold drinks.
The Probability of orange flavored 20/30 = 2/3 = 0.6666....
66.6666....%= 66(2/3) %
please help with word problems.
Answer:
I am sorry but u didn't really ask any question to be answered so next time give a question to be answered
The roots of the equation f(x) = 0 are 1 and -2. The roots of f(2x) = 0) are - - (A) 1 and -2 (B) and - 1 (C) and 1 2 2 (D) 2 and -4 (E) -2 and 4
Answer: B
Step-by-step explanation:
When f(x) turns into f(2x), we need to halve the value of x.
The roots of f(2x) will be equal to ( 1 / 2 ) and -1.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the root of function f(x) are 1 and -2. The roots of F(2x) will be calculated as:-
( x - 1 ) ( x + 2 ) =0
( 2x - 1 )( 2x + 2 ) =0
x = 1 / 2
x = -1
Therefore, the roots of f(2x) will be equal to ( 1 / 2 ) and -1.
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Write an equation for the nth term of this sequence: 1/8, 1/4, 1/2, 1..
Answer:
[tex]a_n=\frac{1}{8} (2^{n-1})[/tex]
Step-by-step explanation:
This is a geometric sequence. You start with the first term, 1/8, then multiply it by 2 to get 1/4, then double that to get 1/2, etc.
The number you multiply by is called the common ratio. In this case, the common ratio is 2.
A formula for the general (nth) term is: [tex]a_n=a_1 r^{n-1}[/tex].
[tex]a_1=1/8\\r=2[/tex]
So the nth term is [tex]a_n=\frac{1}{8} (2^{n-1})[/tex]
If you move from zero to 15 on the number line, you are representing all of the following except
the absolute value of 15
the distance between zero and 15
the opposite of -15
the opposite of 15
Answer: the opposite of 15
Step-by-step explanation:
328 rattle snakes in 2008. How many will there be in 2024?
402853
21498508
32800
20992
Answer:
[tex]{ \tt{12 \: months = 328}} \\ { \tt{(12 \times 15) = \frac{(15 \times 328)}{1} }} \\ \\ = { \tt{4920}}[/tex]
Answer:
2008=328
2024=?
Step-by-step explanation:
12×13 = 16×328/1
PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS! An inheritance of 2 Million was given to a young professional by his parents. He invested the entire amount in real estate, mutual funds, government bonds, and crytocurrencies.
Answer:
a) 17.5%
b) $150,000
c) 27°
Step-by-step explanation:
Angles around a point add up to 360°.
Therefore, to find the percentage of the portion of the pie chart, divide the degree of the portion by 360° and multiply by 100%
Assuming that Real Estate is half of the circle, and Mutual Funds are a quarter of the circle.
a) Government Bonds = (63° ÷ 360°) x 100% = 17.5%
b) Crypto Currency = 90° - 63° = 27°
Therefore, (27° ÷ 360°) x 100% = 7.5%
7.5% of $2,000,000 = 0.075 x $2,000,000 = $150,000
c) Crypto Currency = 90° - 63° = 27°
#a
Find percentage (whole is 360°)
63/360×1000.175(100)17.5%#2
Angle of crypto=180-(90+63)=180-153=27°
Percentage:-
27/360×1000.075(100)7.5%Total
2M(0.075)0.15M150K#c
Found in second part
i'm burfunkled right now
Answer: what grade is this
Step-by-step explanation:
How many milliliters could a container with a volume of 154 cm cubed hold?
A. 0.154 ml
B. 1.54 ml
C. 154 ml
D. 15,540 ml
154 cm3 = 0,154 dm3 = 0,154 l = 154 ml
what is 122 / 600?
[tex]122 \div 600[/tex]
Answer:122/600= 0.20333333333
Step-by-step explanation:
What is the value of x? sin(x 37)°=cos(2x 8)° enter your answer in the box. x =
The value of x which saisfies the equation sin(x+37)°=cos(2x+8)° is 135 or 15.
How to convert sine of an angle to some angle of cosine?We can use the fact that:
[tex]\sin(\theta ^\circ) = \cos(90 - \theta^\circ)[/tex]
to convert the sine to cosine (but the angles won't stay same unless its 45 degrees).
For this case, we're specified the equation sin(x+37)°=cos(2x+8)°.
Converting sine to cosine, we get:
[tex]\cos(90 - x - 37)^\circ = \cos(2x + 8)^\circ\\[/tex]
Since cosine is a periodic function with period of [tex]360^\circ[/tex], thus, we get:
[tex]90 - x - 37= 2x + 8 +360 n[/tex]
where n = an integer (positive, negative, or zero).
or
[tex]90 - 37 - 8= 3x + 360 n\\\\x = \dfrac{45 - 360n}{3} = 15 - 120n[/tex]
This is the general solution of the considered equation.
Assuming that only principal values (from 0 to 360 degrees) angles are allowed, we need:
[tex]0 \leq x + 37 \leq 360\\\\and\\\\0 \leq 2x+8 \leq 360[/tex]
The first inequality gives:
[tex]-37 \leq x \leq 323[/tex]
The second inequality gives:
[tex]-4 \leq x \leq 176[/tex]
We need to satisfy both the inequalities, so the final boundaries on x are:
[tex]-4 \leq x \leq 176[/tex] (the minimum ones for which both inequalities stay true).
n = -2 gives x = 255n = -1 gives x = 135n = 0 gives x = 15n = 1 gives x = -105n < -2 gives x > 255, and n > 1 gives x < -105
So, values of n for which [tex]-4 \leq x \leq 176[/tex] is true are n = -1, or n = 0
Thus, x = either 135 or 15
sin
Thus, the value of x which saisfies the equation sin(x+37)°=cos(2x+8)° is 135 or 15
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After door-to-door canvassing, census workers determine the number of unoccupied homes. The table shown to the
right lists the number of homes, in millions, that were unoccupied in four census years.
Answer questions a through c.
The exponential regression equation of the census predicts the number of unoccupied homes
The exponential regression equation is y = 5.247256 * 1.033157^x
How to determine the exponential regression equation?The dataset is given as:
x y
0 5.3
10 7.3
20 9.7
30 14.3
To determine the exponential regression equation, we make use of a graphing calculator.
The calculation summary from the graphing calculator are:
Regression Equation: y = 5.247256 * 1.033157^xCorrelation: r = 0.998002R-squared: r^2 = 0.996008Hence, the exponential regression equation is y = 5.247256 * 1.033157^x
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Use the distributive property (expand) to write an equivalent expression for: 3(4x-2t). Type your answer ( I NEED THIS RIGHT AWAY PLS)
Answer:
The distributive property here is to just multiply each value by tree number outside the parenthesis.
3 ( 4x - 2t)
12x - 6t
That would be your answer.
In parallelogram MNPQ, m∠M=6x+10°m∠M=6x+10° and m∠N=5x+10.5°m∠N=5x+10.5°. How many degrees is ∠M?
Answer: 97
Step-by-step explanation:
An appliance store sells an oven for 25% off the original price. The sale price is $251.85, not including tax. What is the price of the oven, not including tax, before the discount is applied?
each team in a youth soccer league pays $784 to join the league. if a team consists of 12 players and the fee is divided equally among the players, how much does each player pay?
Answer:
$65.33
Step-by-step explanation:
12x = 784
÷12 ÷12
x = 65.33
They would each have to pay $65.33.
I hope this helps!
Which of the following best explains why one graph appears skewed and one graph appears symmetrical? The scale of the box-and-whisker plot does not start at zero. The interval of the box-and-whisker plot is too large. The interval of the stem-and-leaf plot is not consistent. The scale of the stem-and-leaf plot is too small for the set of data.
The statement that best explains why one graph appears skewed and one graph appears symmetrical is given by: Option C: The interval of the stem-and-leaf plot is not consistent.
What is a symmetric distribution?A symmetric distribution oftenly refers to the distribution which looks symmetric about a fixed line.
For this case, the missing image is attached below.
The stem leaf plot represents the considered bar plot.
But stem leaf plot seems symmetric whereas the box plot isn't.
This is because the stem and leaf plot is missing '5' in its stem, making the interval inconsistent.
Doing inconsistant graphing isn't allowed as that represents distorted data, as for this case, the data seems symmetric when it isn't.
Thus, the statement that best explains why one graph appears skewed and one graph appears symmetrical is given by: Option C: The interval of the stem-and-leaf plot is not consistent.
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Answer:c edge
Step-by-step explanation:
In rectangle GRAM below GA =4×+17 and MR= 7x-4 find the value of x and the lenghts of GA MR
Answer: x=7, GA=MR=14
Step-by-step explanation:
What is the area and perimeter for this ?
Answer:
Step-by-step explanation:
The area of a parralelogram is B*H
Base is 20.2
Hight is 12
20.2*12=242.4
Perimeter is the sum of all sides
20.2*2+12*2=64.4
Alison had 310 rocks in her rock collection. After three months, her collection increases by 40%. How many rocks does Alison have now?
Answer:
434
Step-by-step explanation:
310 times .4 (percentage) = 124 which is how much she gained, then you add that onto the original amount to find how many she has now, which is 434
Eric runs a coffee shop and bought 5,480 cups at the beginning of the week. At the end of the week, he had 20% of the cups left. How many cups does Eric have left?
Answer: 1,096 cups
Step-by-step explanation:
Answer: 1096 cups left.
Step-by-step explanation: 20% of 5,480 is 1096. This is accurate because 20% is one-fifth of 100%. In this case, 5,480 is our 100%. When you divide 5,480 by 5, you get the answer 1,096, which is 20% of the 5,480 cups that Eric started with.
Have a great day! :)
how would you solve this
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's write the equation in standard form ~
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + {y}^{2} - 2y - 15 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \:(x ){ }^{2} + {y}^{2} - 2y = 15[/tex]
[tex]\qquad \sf \dashrightarrow \:(x ){ }^{2} + {y}^{2} - 2y + 1 = 15 + 1[/tex]
[tex]\qquad \sf \dashrightarrow \:(x ){ }^{2} +( {y}^{} - 1 ) {}^{2} = 16[/tex]
Now, it's the required form of circle ~