Answer:
2313
Step-by-step explanation:
The data obtained from a random sample of track athletes showed that as the foot size of the athlete decreased, the average running speed decreased. Which statement is best supported by the data?Immersive Reader
Answer:
The correct option is;
(3) The sample of track athletes show that there is a correlation between foot size and running speed
Step-by-step explanation:
The statements are analysed as follows;
(1) Smaller foot sizes cause track athletes to run slower.
The above statement is a conclusion and it infers more information than is contained in the question statement because there are other factors such as taller athletes run faster than average sized athletes
(2) The sample of track athletes shows a causal relationship between
foot size and running speed.
The above statement is similar to the one above as it is a milder conclusion and it infers more information than is contained in the question statement
(3) The sample of track athletes shows a correlation between foot size
and running speed.
The above statement is correct as is directly supported by the data as it is a statement made based directly the data
(4) There is no correlation between foot size and running speed in
track athletes.
The above statement is not supported by the available data.
A number, n, decreased by 14 equals
60. Write an equation and solve for n.
Answer:
n=74
Step-by-step explanation:
The equation would be:
n-14=60
Decreased means subtraction, so 14 is being subtracted from n, and it is equal to 60.
Solve for n, by isolating n.
To do this, add 14 to both sides
n-14+14=60+14
n=74
carmen weight 96 pound. Her sister weighs 29 pounds less than carmen.together they weigh 33 pounds less than their dad. how much does carmen sister weight
Answer:
Their dads weight is not important don't body shame him peeps. 96-29=67, therefore that is how much she weighs, leaving out the unnecessary info.
Step-by-step explanation:
Researchers are studying two populations of sea turtles. In population D, 30 percent of the turtles have a shell length greater than 2 feet. In population E, 20 percent of the turtles have a shell length greater than 2 feet. From a random sample of 40 turtles selected from D, 15 had a shell length greater than 2 feet. From a random sample of 60 turtles selected from E, 11 had a shell length greater than 2 feet. Let pˆD represent the sample proportion for D, and let pˆE represent the sample proportion for E.
(a) What is the value of the difference pˆD−pˆE? Show your work.
Answer:
[tex]p^D-p^E=0.192[/tex]
Step-by-step explanation:
We are given the following in the question:
Population D:
30% of the turtles have a shell length greater than 2 feet.
Sample size,
[tex]n_D = 40[/tex]
Number of turtles that had shell length greater than 2 feet,
[tex]x_D = 15[/tex]
Sample proportion:
[tex]p^D=\dfrac{x_D}{n_D} =\dfrac{15}{40} = 0.375[/tex]
Population E:
20% of the turtles have a shell length greater than 2 feet.
Sample size,
[tex]n_E = 60[/tex]
Number of turtles that had shell length greater than 2 feet,
[tex]x_E = 11[/tex]
Sample proportion:
[tex]p^E=\dfrac{x_E}{n_E} =\dfrac{11}{60} = 0.183[/tex]
We have to find the difference between the sample proportion.
Difference in sample proportion =
[tex]=p^D-p^E\\=0.375-0.183\\=0.192[/tex]
. You and your friend are playing the following game: two dice are rolled; if the total showing is
divisible by 3, you pay your friend $6. How much should he pay you when the total is not divisible
by 3 if you want to make the game fair? A fair game is one in which your expected winnings are
$0.
Answer:
3$
Step-by-step explanation:
Because every 3 numbers are divisble by 3 and the other 2 are not. Then the chance of you winning is 66%, therefore he should pay you half of what he would make. If this makes sense.
What is reasonable estimate for the problem
Answer:
-2
Step-by-step explanation:
this is i ready lol but basically the actual answer is -1.5 but if you round that you get -2
Answer:
-2
Step-by-step explanation:
3 3/4 times -2/5 = -1.5, which is closer to -2.
A computer is generating passwords. The computer generates six characters at random, and each is equally likely to be any of the letters or digits. Replications are allowed. What is the probability that the password will contain all letters?
Answer:
0.1419 ( (if upper and lower cases are interchangeable)
0.348 ( if upper and lower cases are distinct letters)
Step-by-step explanation:
Each digit has 36 possible choices as 26+10
computer generates six characters
there are only 26 choices for letters only, (if we assume upper and lower cases are interchangeable)
For number of letters-only arrangements = [tex]26^{6}[/tex] = 308915776
For number of alphanumeric arrangements = [tex]36^{6}[/tex]= 2176782336
In order to find the probability of letters-only arrangements : [tex]\frac{308915776}{2176782336}[/tex]
=>0.1419
Now, in different scenario if upper and lower cases are not interchangeable.
We will have 26+26+10=62 alphanumeric choices, and 52 alphabetic choices
Therefore, probability of letters-only arrangements will be [tex]\frac{52^{6} }{62^{6} }[/tex]
=>0.348
Answer:
The probability of all letters arrangement if the upper cases and the lower cases of the English alphabet are interchangeable = 14.2%
The probability of all letters arrangement if the upper cases and the lower cases are not interchangeable = 34.8%
Step-by-step explanation:
please kindly check the attached files for explanation.
A box plot is shown below: A box and whisker plot is shown using a number line from 20 to 45 with primary markings and labels at 20, 25, 30, 35, 40, 45. In between two primary markings are 4 secondary markings. The box extends from 27 to 38 on the number line. A line in the box is at 32. The whiskers end at 20 and 42. The title of the art is Visitors at the Exhibition, and below the line is written Number of Visitors. What is the median and Q1 of the data set represented on the plot?
Median = 30; Q1 = 27
Median = 32; Q1 = 27
Median = 30; Q1 = 20
Median = 32; Q1 = 20
Answer:
b) Median 32; Q1 =27
Step-by-step explanation:
The description to the left directs us how to draw the box and whiskers. Using the markings. 20, 25, 30, 35, 40,45 check on the left side of the graph.The box extends from 27 to 38 on the number line. So, that means Q1=27 and Q3=38The whiskers end at 20 and 42. The minimum and the Maximum value of the Distribution, the "whisker".A line in the box is at 32. The horizontal line the slices the box, in other words the Median.So here it is, our Box and Whiskers Plot.
A special deck of cards consists of 5 red cards, 20 blue cards, and 25 green cards. Svetlana selects 1 card from the special deck 500 times. How many times can she expect to draw a red card?
Answer:The answer is 50
Step-by-step explanation:
The first step is to add up the numbers in order to get the outcome
5 red + 20 blue +25 green =5+20+25 =50
Step 2
Probability =no of events /no of outcome
We were asked to find the probability of red
Where red represent event
And the summation of red ,green and blue represents outcome .
So probability of red =5/50 = 1/10
Step 3
Recall in the question ,we were told that the card was selected 500 times ,so we multiply the probability of getting red by 500
1/10 *500 =50
Therefore the probability of drawing a red card from the special deck 500 times is 50 .
Gabriella has the following winter accessories:
1 winter coat: black
2 hats: blue, purple
2 pairs of boots: black, brown
5 pairs of mittens: black, blue, purple, red, white
Find the probability of wearing the coat with the purple hat, black boots, and purple mittens.
Answer:
1/20
Step-by-step explanation:
There are 20 possible probabilites/combinatins of what to wear, and wearing a coat, with a purple hat, black boots, and purple mittens is only 1 of those 20 probabilities so the answer is 1/20
A smartphone costs $280. sales tax is 5%. What is the total cost,including tax?
Answer:
$294
Step-by-step explanation:
1 is equivalent to 100% which would mean .05 is equivalent to 5%.
Therefore, multiply the base cost by 1.05 to find the total cost.
$280 x 1.05 = $294
i need the steps for 25
Answer:
3/5
Step-by-step explanation:
The scale factor is found by taking the ratio of coresponding sides
side of triangle HKM
--------------------------------
side of triangle DFG
HK
---------
DF
18
----
30
3
----
5
Answer:
51°
Step-by-step explanation:
Angle K corresponds to Angle F
Angle F = 180 - 70 - 59
Angle F = 51°
30% of 750 using an table
Answer:
225
Step-by-step explanation:
30%×750 = 30×750/100 = 3×75 = 225
Answer:
525
Step-by-step explanation:
10%= 75 (750 divided by 10)
30%= 225 (75 x 3)
750-225= 525
What is the measure of
Answer:
A: 28
Explanation:
Vertical angles are congruent.
Answer:
The answer would be 28% because the angles are vertical, which also makes them congruent. Congruent angles have the same angle measure.
Find the solution
2cos2x-2cosx=0
Answer:
x = 0, 2π/3, 4π/3
Step-by-step explanation:
2 cos(2x) − 2 cos x = 0
Use double angle formula.
2 (2 cos²x − 1) − 2 cos x = 0
Simplify.
4 cos²x − 2 − 2 cos x = 0
2 cos²x − 1 − cos x = 0
2 cos²x − cos x − 1 = 0
Factor.
(cos x − 1) (2 cos x + 1) = 0
Solve.
cos x = 1 or -½
x = 0, 2π/3, 4π/3
To solve this problem, we have to use trigonometric function in which we can use some trigonometric equations on this. The solutions to this equation is
[tex]\pi , \frac{\pi}{3}, \frac{5\pi}{3}[/tex]
Trigonometric FunctionsWe would apply a simple mathematical rule here;
[tex]a(b+c)=ab+ac[/tex]
Let's substitute our functions and solve
[tex]2cos(2x)+2cosx=0\\2(2cos^2x-1)+2cosx=0\\4cos^2x-2+2cosx=0\\2cos^2x+cosx-1=0\\2cos^2x=2cosx-cosx-1=0\\2cos^2x+cosx-1=0\\[/tex]
We can solve the quadratic equation and get a solution to this problem.
[tex](cosx+1)(2cosx-1)=0[/tex]
Using factorization method,
[tex]cosx+1 = 0\\cosx = -1\\x = cos^-^1(-1)\\x = \pi[/tex]
The second solution is
[tex]2cosx-1=0\\2cosx=1\\cosx=\frac{1}{2} \\x = cos^-^1(\frac{1}{2} \\x = \frac{\pi}{3}, \frac{5\pi}{3}[/tex]
From the above calculations, the solutions to this equation is
[tex]\pi , \frac{\pi}{3}, \frac{5\pi}{3}[/tex]
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Jalen is computing the slope of a line on the graph below. Which statement describes Jalens error?
Jalen computed the raitio in e to change in y
Jalen use the ordered pairs in the wrong order
Jalen made a computational error
Jalen used an ordered pair that is not on the line
Answer:
A
Step-by-step explanation:
Have a nice day everyone
The slope value calculated by Jalen is not correct. Jalen has used the ordered pairs in the wrong order.
What is the point slope form of a line ?
Point slope form is used to represent a straight line using its slope and a point on the line.
It is given that Jalen is computing the slope of a line.
We know that the equation of a line in point slope form is given by :
(y - y1) = m (x - x1).
As per the computation done by Jalen ordered pairs are (-4, 0) and (2, 3).
For the line : (x , y) = (4 , 0) and (x1 , y1) = (2 , 3).
So ,
Slope will be equal to :
m = (y - y1) / (x - x1)
m = (0 - 3) / (4 - 2)
m = -3 / 2
So , the slope calculated by Jalen is not correct as he has used the ordered pairs in the wrong order.
Therefore , the slope value calculated by Jalen is not correct. Jalen has used the ordered pairs in the wrong order.
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Jackie makes silver and gold charms for charm bracelets. The charms are similar isosceles triangles. The gold charm has a base of 6 mm and an area of 15 mm. The silver charm has a base of 9 mm. What is the area of the silver char
Answer:
The area of silver charm is 33.75 square mm.
Step-by-step explanation:
We are given the following in the question:
The silver and golden charms are similar isosceles triangles.
Gold charms:
Base = 9 mm
Area = 15 square mm
Silver charm:
Base = 9 mm
Property of similar triangles:
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.Using this property we can write:
[tex]\dfrac{\text{Area of gold charm}}{\text{Area of silver charm}}=\dfrac{(\text{Base of gold charm})^2}{(\text{Base of silver charm})^2}\\\\=\dfrac{15}{\text{Area of silver charm}}=\dfrac{6^2}{9^2}\\\\\text{Area of silver charm} = \dfrac{15\times 9^2}{6^2} = 33.75\text{ mm}[/tex]
Thus, the area of silver charm is 33.75 square mm.
Mildred has a bag of coins. The bag contains 10 dimes, 5 nickels, and 1 penny. She will randomly select 2 coins from the bag one at a time without replacement. What is the probability that Mildred will select a dime first and then a month penny?
The probability that Mildred will select a dime first and then a month penny is 1/24.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total possibilities = 16
So, Probability of a dime of the first draw = 10/16 = 5/8
and, Probability of a penny on the second draw = 1/15
Thus, Probability of both = 5/8 x 1/15
= 1/24
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The probability that Mildred will select a dime first and then a penny is 1/24.
To calculate the probability that Mildred will select a dime first and then a penny from her bag of coins, we need to consider the following steps:
1. Probability of selecting a dime first:
- Mildred has a total of 10 dimes, 5 nickels, and 1 penny in the bag.
- The probability of selecting a dime on the first draw is the number of dimes divided by the total number of coins, which is 10 dimes out of 16 total coins.
2. Probability of selecting a penny next:
- After selecting a dime on the first draw, Mildred will have 9 dimes, 5 nickels, and 1 penny remaining in the bag.
- The probability of selecting a penny on the second draw is the number of pennies divided by the total number of remaining coins, which is 1 penny out of 15 remaining coins.
3. To find the overall probability, we multiply the individual probabilities:
- Probability = (Number of dimes / Total coins) * (Number of pennies / Remaining coins)
- Substituting the numbers, we get (10/16) * (1/15) = 1/24.
Therefore, the probability that Mildred will select a dime first and then a penny is 1/24.
is you add up 1:03:25, 2:06:41 and 2:09:12. what is the total in hrs mins and secs?
Answer:
5 hours 19 minutes 18 seconds
Step-by-step explanation:
Answer:
5:19:18
Step-by-step explanation:
factor the expression
Step-by-step explanation:
Given
6x² + 5x + 1
= 6x² + ( 2 + 3)x + 1
= 6x² + 2x + 3x + 1
= 2x ( 3x + 1 ) + 1 ( 3x + 1)
= ( 3x + 1) ( 2x +1)
Hope it will help :)
Your credit card debt to limit ratio has a huge impact on your FICA score (30%). It should always be kept below 15%. If your card has a limit of $3,000 and your credit card debt has reached it, what payment will you need to apply to your balance to pay it down to 15%?
Answer:
The amount of payment that needs to be applied to the debt balance to bring the debt to limit ratio to 15% is $2,250
Step-by-step explanation:
Here we have the card limit as $3,000
The card debit to limit ratio should be kept below 15%
Therefore, card limit of $3,000 = 100%
The protect FICA score card debt to limit ratio required required is 15% that is;
Maximum appropriate card debt is 15% of Max allowable card debt
Maximum appropriate card debt = 15% of $3,000 = $450.00
Current debt on card = $3,000
Payment to be applied to the balance to pay it down to 15% is given by
[tex]\$3,000 - \frac{15}{100} \times \$3000 = \$3,000 - \$450 = \$2550[/tex]
Therefore a $2,550 payment will be applied to the balance to pay it down to 15%.
Final answer:
To reduce your credit card debt to 15% of a $3,000 limit, you would need to make a payment of $2,550. This is calculated by determining 15% of the limit and subtracting it from the current balance to find the necessary payment amount.
Explanation:
Calculating Payment to Lower Credit Card Debt to Ratio
If your credit card has a limit of $3,000 and you wish to keep your credit card debt to limit ratio below 15%, first determine what 15% of your credit limit is. Calculate 15% of $3,000, which is $450. Since your current balance is the full limit of $3,000, subtract the target balance of $450 from $3,000. The result is the payment needed to reduce your debt to within the desired ratio.
$3,000 * 0.15 = $450 (15% of your credit limit)
$3,000 - $450 = $2,550
Therefore, a payment of $2,550 will bring your balance down to 15% of the credit limit. Managing your credit utilization is important not just for meeting the credit score components but also for maintaining good financial health.
Which equation demonstrates the distributive property? A) 2 (5 + 7) = 2 (7 + 5) B) 2 (5 + 7) = 2 × 5 + 2 × 7 C) (2 × 5) × 7 = 2 × (5 × 7) D) 7 × (2 × 5) = 7 × (5 × 2)
Answer:
B
Step-by-step explanation:
got it right on momentum
Calculate the area of this triangle.
13 cm
5 cm
-12 cm-
Answer:
30 cm^2.
Step-by-step explanation:
This is a right angled triangle because it fits the Pythagoras theorem ( 13^2 = 12^2 + 5^2).
The area = 1/2 * 12 * 5
= 30 cm^2.
Use these functions to evaluate the following problems: f(x) = x, g(x) = x - 3, h(x) = x^2 - 9, k(x) = 2x
(hk)(x)
(k/f)(x)
(h/g)(x)
Answer:
(hk)(x) = 2x³-18x
(k/f)(x) = 2
(h/g)(x) = x+3
Step-by-step explanation:
(hk)(x)
(x² - 9)(2x)
2x³ - 18x
(k/f)(x)
2x/x
2
(h/g)(x)
(x² - 9)/(x - 3)
[x² - 3²]/(x - 3)
(x + 3)(x - 3)/(x - 3)
x + 3
A town covers a 50.5 square mile area. If they population density of the town is 48.2 people per square mile, what is the population of the town, to the nearest hundred people.
Answer:
The population of town is approximately 2400 people.
Step-by-step explanation:
We are given the following in the question:
Area of town = 50.5 square miles
Population density of town = 48.2 people per square mile
Population of town =
[tex]P= \text{Area}\times \text{Population density}\\P=50.5\times 48.2\\P=2434.1[/tex]
Now, we have to round off this population to nearest hundred.
After rounding off,
[tex]P=2400\text{ people}[/tex]
Thus, the population of town is approximately 2400 people.
A phone company offers two monthly plans. Plan A costs $9 plus an additional $0.17 for each minute of calls. Plan B costs$25 plus an additional $0.15 for each minute of calls. For what amount of calling do the two plans cost the same?
Answer:
800 minutes
Step-by-step explanation:
Make 2 expressions, one for Plan A, and one for Plan B
Plan A:
$9, and 0.17 per minute
9+0.17x
Plan B:
$25, and 0.15 per minute
25+0.15x
We want to find when they are the same, so we can set them equal to each other
9+0.17x=25+0.15x
Solve by isolating the variable, x
Subtract 9 from both sides
0.17x=16+0.15x
Subtract 0.15x from both sides
0.02x=16
Divide both sides by 0.02
x=800
At 800 minutes they will cost the same
Find the length of the darkened arc. Leave your answer in terms of pi.
Answer:
[tex] \frac{15 }{4} \pi \:[/tex]
Step-by-step explanation:
Radius of circle (r) = 18/2 = 9 ft
Central angle = 180° - 30° = 150°
[tex]length \: of \: arc \\ = \frac{150 \degree}{360 \degree} \times 2\pi \: r \\ \\ = \frac{150 \degree}{360 \degree} \times 2 \times \pi \: \times 9\\ \\ = \frac{5 }{12 } \times 18 \times \pi \: \\ \\ = \frac{5 }{4} \times 3\times \pi \:\\ \\ = \frac{15 }{4} \pi \:[/tex]
The length of the darkened arc can be found using the formula s = Δθr, where s is the length of the arc, Δθ is the angle of rotation, and r is the radius of curvature.
Explanation:The length of the darkened arc can be found by using the formula for arc length: s = Δθr, where s is the length of the arc, Δθ is the angle of rotation, and r is the radius of curvature. In this case, the angle of rotation is 2π radians (since it is a complete revolution) and the radius is given. So, substituting these values into the formula, we have s = 2πr.
Which inequality is true when x = 4
A. x + 5 < 3
B. 9x > 36
C. ×/2 < 3
D. 18 < x + 8
Answer:
A
Step-by-step explanation:
One inequality could be x > 3. So when x = 4 this is true because 4 is greater than 3.
The solution is Option C.
The value of the inequality equation x/2 < 3 is true when x = 4
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
a)
Let the inequality equation be
x + 5 < 3
when the value of x = 4
Substitute the value of x as 4 in the equation , we get
4 + 5 < 3
9 < 3 is not true
b)
Let the inequality equation be
9x > 36
when the value of x = 4
Substitute the value of x as 4 in the equation , we get
36 > 36
36 > 36 is not true
c)
Let the inequality equation be
x/2 < 3
when the value of x = 4
Substitute the value of x as 4 in the equation , we get
4/2 < 3
2 < 3 is true
d)
Let the inequality equation be
18 < x + 8
when the value of x = 4
Substitute the value of x as 4 in the equation , we get
18 < 4 + 8
18 < 12 is not true
Hence , the inequality equation is x/2 < 3 when x = 4
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Help please!!
How many lines of symmetry does the following figure have?
1) 16
2) 2
3) 8
4) 4
Answer:
4
Step-by-step explanation:
Symmetry is when you can flip the figure over a line and it will perfectly match the other side.
We see that if we draw a vertical line down the middle and a horizontal line across the middle, we get mirror images. So that's 2.
Then notice that we can draw two diagonals across the image, one from the upper left corner to the lower right corner and the other from the upper right corner to the lower left corner. That's another 2.
We try to find more, but try as we might, there are no others to be found.
Thus, there are 4 lines of symmetry.
Hope this helps!
In ΔVWX, the measure of ∠X=90°, VX = 35, XW = 12, and WV = 37. What is the value of the cosine of ∠W to the nearest hundredth?
Answer:
Cosine W = 0.32
Step-by-step explanation:
Adj/Hypo = 12/37 = 0.3243 = 0.32
Final answer:
The cosine of ∠W in triangle ΔVWX is found by dividing the length of the side adjacent to ∠W (XW) by the length of the hypotenuse (WV), resulting in cos(∠W) ≈ 0.32 to the nearest hundredth.
Explanation:
In triangle ΔVWX, where ∠X=90°, VX = 35, XW = 12, and WV = 37, we are asked to find the value of the cosine of ∠W to the nearest hundredth. Since ∠X is a right angle, this triangle is a right triangle, and we can use trigonometric ratios to find the cosine of ∠W. The cosine of an angle in a right triangle is equal to the adjacent side over the hypotenuse.
To find the cosine of ∠W, we look at the sides adjacent to ∠W, which are XW and WV. The length of XW is 12, and WV, being the hypotenuse, is 37. Therefore, to find cos(∠W), we calculate 12/37. Doing this calculation, we get cos(∠W) ≈ 0.32 to the nearest hundredth.
The cosine is a trigonometric function that relates the lengths of sides in a right triangle to the angles, and it is specifically the ratio of the length of the adjacent side to the length of the hypotenuse.