Answer:
The jogging rate of Matthew is 5 mph.
Step-by-step explanation:
Let the jogging rate of Matthew be x mph.
It is given that his jogging rate was 25 mph slower than the rate when he was riding. So, the riding rate is (x+25) mph.
The distance between Matthew and his friend's house is 12 miles.
[tex]Speed=\frac{Distance}{Time}[/tex]
[tex]Time=\frac{Distance}{Speed}[/tex]
The time taken by Matthew in jogging is [tex]\frac{12}{x}[/tex] and the time taken by Matthew in riding is [tex]\frac{12}{x+25}[/tex].
It took him 2 hours longer to jog there than ride back.
[tex]\frac{12}{x}=\frac{12}{x+25}+2[/tex]
[tex]\frac{12}{x}-\frac{12}{x+25}=2[/tex]
[tex]\frac{12(x+25)-12x}{x(x+25)}=2[/tex]
[tex]12x+300-12x=2x(x+25)[/tex]
[tex]300=2x^2+50x[/tex]
[tex]0=2x^2+50x-300[/tex]
[tex]0=x^2+25x-150[/tex]
[tex]0=x^2+30x-5x-150[/tex]
[tex]0=(x+30)(x-5)[/tex]
Equate each factor equal to 0.
[tex]x=5,-30[/tex]
The speed cannot be negative, therefore the jogging rate of Matthew is 5 mph.
Answer:
the answer is D
Step-by-step explanation:
evaluate the expression when w=3,x=-2,y=6 and z=0.5
yz/w + 2x
Substitute the values of w, x, y and z to the expression:
[tex]w=3,\ x=-2,\ y=6,\ z=0.5\\\\\dfrac{yz}{w}+2x=\dfrac{(6)(0.5)}{3}+(2)(-2)=\dfrac{3}{3}-4=1-4=-3[/tex]
Answer: -3
Step-by-step explanation:
chloe made a conjecture that given any two numbers, the greater number can always be arranged into more arrays.
State whether you agree or disagree. Then explain why you think so by giving an example of two numbers that prove or disprove the conjecture.
Solution:
Array means arrangement of numbers in terms of rows and columns.
The conjecture is not True.
So, the conjecture made by chloe that given any two numbers, the greater number can always be arranged into more arrays is not true.
For example ,
1.(2,3)
2→(2×1),(1×2)
3→(3×1),(1×3)
This pair has same number of arrays because both of them are prime.
2. (3,4)
Here, 4>3
3→ (3 × 1),(1×3)
4→(4×1),(1×4),(2×2)
The pair of numbers are Co-prime, one of them is not prime. So Composite number has more number of arrays.
4. (6,11)
6→(1×6),(6×1),(2×3),(3×2)
11→(1×11),(11×1)
The number 6 is smaller, but it has more number of arrays.
5. (6,8)
6→(1×6),(6×1),(2×3),(3×2)
9→(1×9),(9×1),(3×3)
Both the numbers are composite.Smaller number 6 has more arrays.
These examples disprove the Conjecture made by Chloe, which states that given any two numbers, the greater number can always be arranged into more arrays.
What is the answer to -282=-6(5+7x)
Answer:
x = 6
Step-by-step explanation:
We have to isolate x.
-282 = -6(5+7x)
Distribute.
-282 = -30 - 42x
Add 30 to both sides.
-252 = -42x
Divide both sides by -42.
6 = x
Karla can buy guppies for $0.90 each at the corner pet store. If she has $13.50, how many guppies can she buy?
All we have to do here is divide $13.50 by $0.90 to figure out how many guppies she can buy
$13.50 ÷ $0.90 = 15
Therefore, Karla can buy 15 guppies with $13.50
Hope this helps you
Brainliest would be appreciated
- AaronWiseIsBae
Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10. In what percentile is a score of 65?
Answer:
30.85%
Step-by-step explanation:
Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10
mean = 70 and SD= 10
To find percentile we use z-score value
z value can be find using formula
[tex]z= \frac{x-mean}{SD}[/tex]
[tex]z= \frac{65-70}{10}[/tex]
z=-0.5
Now we use z- score table to find the value when z=-0.5
P(x=65) = 0.3085
To find percentile we multiply by 100
0.3085 * 100 = 30.85%
A student randomly draws a card from a standard deck and checks to see if it is his favorite suit he then returned to card to the deck shuffles and repeats experiment he performs experiment 30 times can the probability of drawing his favorite suit be found by using the binomial probability formula why or why not
Answer:
The binomial probability formula can not be used for this experiment because it does not state the number of times he expects to draw his favorite suit.
Step-by-step explanation:
The binomial probability formula is expressed as follows:
P (k success in n trials) = [tex]\left \{ {{n \atop k} \right.[/tex] [tex]p^{k}[/tex][tex]q^{n-k}[/tex]
n = number of trials, k = number of successes, n-k = number of failures, p = probability of success in one trial and q = 1 - p = probability of failure in one trial.
In the given problem, all of the variables are known except for 'k', the amount of times that the student predicts he will draw his favorite suit.
Yes, the student's card drawing experiment can be considered a binomial experiment and therefore the binomial probability formula can be applied. This is because there are two possible outcomes for each trial (success or failure), the trials are independent, and the number of trials is fixed.
Explanation:Yes, the probability of drawing his favorite suit can be found by using the binomial probability formula. This is because the scenario described satisfies the conditions necessary for a binomial experiment.
First, there are only two possible outcomes for each trial - success (drawing his favorite suit) and failure (not drawing his favorite suit). In a standard deck of 52 cards with 4 suits, there are 13 cards of each suit. Therefore, the probability of success, p, is 13 out of 52, or 0.25 and the probability of failure, q, is 1 - p, or 0.75.
Second, the student performs the experiment 30 times. This means there are a fixed number of independent trials (n = 30). This is independent because he returns the card to the deck and shuffles after each draw, so the outcome of one trial does not affect the outcomes of the other trials.
In a binomial experiment, the random variable X represents the number of successes in n independent trials. The mean, µ, can be calculated using the formula µ = np, and the standard deviation, σ, is given by the formula σ = √npq. Thus, you can use the binomial probability formula to calculate the probability of drawing his favorite suit a certain number of times out of the 30 trials.
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HELP PLEASE! solve for x and y.
Answer:
x=24
y = 8 sqrt(3)
Step-by-step explanation:
Since this is a right triangle, we can use sin and cos
sin 30 = opposite/ hypotenuse
sin 30 = y/ 16 sqrt(3)
Multiply each side by 16 sqrt(3)
16 sqrt(3) * sin 30 = y
16 sqrt(3) * 1/2 = y
8 sqrt(3) = y
cos 30 = adjacent/ hypotenuse
= x/16 sqrt(3)
Multiply each side by 16 sqrt(3)
16 sqrt(3) cos 30 = x
16 sqrt(3) * (sqrt(3)/2) = x
8 * sqrt(3)*sqrt(3)
8 * 3 = x
24 =x
is the length of MN on graph
Answer:
mn=[tex]\sqrt{40}[/tex]
Step-by-step explanation:
m(2,5)n=(4,-1)
[tex]mn^{2}[/tex]=[tex](4-2)^{2}[/tex]+[tex](5+1)^{2}[/tex]
[tex]mn^{2}[/tex]=40
mn=[tex]\sqrt{40}[/tex]
Remy drinks 214 cups of water every 145 hours.
How many cups of water does he drink in 1 hour?
Enter your answer as a mixed number. For example, if your answer is 4212, enter 42 1/2
Answer:
1 69/145 cups
Step-by-step explanation:
We can use ratio's to solve this problem. We will put water over time
214 cups x cups
--------------- = --------------
145 hours 1 hours
Using cross products
214 *1 =145 x
Divide both sides by 125
214/145 = 145x/145
214/145 = x
145 goes into 215 1 time with 69 left over
1 69/145
Which of the following inequalities matches the graph?
Write the equation of a line in slope intercept form that is parallel to 2x + 4y = 10 and passes through the point (8, 2).
A) 16x + 8y = 10
B) y = −12x + 6
C) y = −12x+2
D) y=8x + 2
Answer:
y = -1/2 x + 6
Step-by-step explanation:
2x + 4y = 10
4y = -2x + 10
y = -1/2 x + 5/2
Parallel lines, slope is the same = -1/2
passes through the point (8, 2) so
y - 2 = -1/2(x - 8)
y - 2 = -1/2 x + 4
y = -1/2 x + 6
Answer:
y = -1/2x + 6
Step-by-step explanation:
We know that the slope intercept form of a line is [tex]y=mx+c[/tex].
Also, if two lines are parallel, they have the same slope. So re-writing the given equation 2x + 4y = 10 in the slope intercept form to find know its slope.
[tex]2x + 4y = 10\\\\4y=-2x+10\\\\y=\frac{-2}{4} +\frac{10}{4}\\ \\y=\frac{-1}{2} +\frac{10}{4}[/tex]
So the slope of the equation will be [tex]-\frac{1}{2}[/tex].
Finding the y-intercept (c):
[tex]y=mx+c\\\\2=-\frac{1}{2} (8)+c\\\\c=6[/tex]
Therefore, the equation of the line n slope intercept form that is parallel to 2x + 4y = 10 and passes through the point (8, 2) is y = -1/2x + 6.
Given: ∆ABC, m∠C = 90° AL - is an angle bisector m∠ABC = 30°, LB = 18m Find: CL
Answer:
CL=9
Step-by-step explanation:
I'm sorry I can't explain it but the answer is 9.
The measure of CL is 9 m.
Given that, in ∆ABC, m∠C= 90° AL is an angle bisector m∠ABC = 30°, LB = 18 m.
We need to find the measure of CL.
What is an angle bisector?The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.
Now, sin 30°=CL/BL
⇒ 1/2 = CL/18
⇒ CL=9 m
Therefore, the measure of CL is 9 m.
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Based on the polynomial reminder theorem, what is the value of the function when x= -5
F (x)= x^4 + 12x^3 + 30x^2 - 12x + 70
Answer:
-15
Step-by-step explanation:
Given is a polynomial in x
[tex]F (x)= x^4 + 12x^3 + 30x^2 - 12x + 70[/tex]
We have to find the remainder when the above polynomial is divided by x+5
Remainder theorem says that f(x) gives remainder R when divided by polynomial x-a means f(a) = R
Applying the above theorem we can say that value of the function when x =-5
= Remainder when f is divided by x+5
= F(-5)
Substitute the value of -5 in place of x
= (-5)^4 + 12(-5)^3 + 30(-5)^2 - 12(-5) + 70
= 625-1500+750+60+70
= 5
Hence answer is 5
Answer:
[tex]f(-5)=[/tex] 5
Step-by-step explanation:
According to the polynomial remainder theorem, when a polynomial f(x) is divided by a linear polynomial (x - a), the remainder of that division will be equal to f(a).
Therefore, substituting the value of x as -5 in the given function to find its value:
[tex]f(x)[/tex] = [tex]x^4 + 12x^3 + 30x^2 - 12x + 70[/tex]
[tex]f(-5)[/tex] = [tex](-5)^4 + 12(-5)^3 + 30(-5)^2 - 12(-5) + 70[/tex]
[tex]f(-5)[/tex] = [tex]625+(-1500)+750-(-60)+70[/tex]
[tex]f(-5)[/tex] = [tex]5[/tex]
Therefore, the value of the given function when x = -5 is 5.
Sylvie has a leather cord that is 30 inches long. She needs 6 inches of leather to make a bracelet. How much leather cord will Sylvie have after she removes 6 inches?
Answer:
30-6=24
Step-by-step explanation:
Subtract the 6 inches from the 30 inches.
The functions f(x) = (x + 1)^2 - 2 and g(x) = -(x-2)^2 + 1 have been rewritten using the completing-the-method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.
Answer:
see explanation
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
• If a > 0 then the vertex is a minimum
• If a < 0 then the vertex is a maximum
f(x) = (x + 1)² - 2 → has a > 0
vertex = (- 1, - 2 ) and is a minimum
g(x) = - (x - 2)² + 1 → has a < 0
vertex = (2, 1 ) and is a maximum
Simplify the expression.
x^3/2/x^1/2
[tex]Use\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{x^{\frac{3}{2}}}{x^{\frac{1}{2}}}=x^{\frac{3}{2}-\frac{1}{2}}=x^{\frac{3-1}{2}}=x^{\frac{2}{2}}=x^1=x\\\\Answer:\ \boxed{x}[/tex]
Shelly types 301 words in 3 1/2 minutes what is the rate at which Shelly types in words per minute
Answer:
86 wpm
Step-by-step explanation:
You need to set up a proportion
x words in 1 minute301 words in 3.5 minutesx/1 = 301/3.5x = 301 / 3.5x = 86 words / minuteAnswer:
86 words per minute
Step-by-step explanation:
You would divide 301 by 3 1/2 to find the unit rate. The answer will be 86. So Shelly types 86 words per minute.
The spoke of wheel reaches from the center of the wheel to its rim if the circumstance of the wheel is 48 inches, how long is each spoke? Use 3.14 for and round your answer to the nearest hundredth.
Answer:
7.6 in
Step-by-step explanation:
c = 2πr Divide each side by 2π
r = C/2π Insert values
r = 48/(2×3.14)
r = 48/6.28
r = 7.6 in
A population of bacteria increases by 30 every hour. Is this situation linear or exponential? A. Exponential, because the function grows by a common factor B. Exponential, because the function decreases C. Linear, because the function decreases D. Linear, because the function increases by a constant amount
Answer:
The correct option is D.
Step-by-step explanation:
In a linear function the rate of change is constant. It means either the function increase by a constant rate or function decrease by a constant rate.
In an exponential function the rate of change is not constant.
It is given that the population of bacteria increases by 30 every hour.
Since the population of bacteria increases by a constant rate therefore the population function is linear and it is defined as
[tex]P(t)=P_0+30t[/tex]
Where P₀ is initial population and t is time in hours.
Therefore correct option is D.
In the situation where a population of bacteria increases by a constant amount every hour, the growth pattern is linear, not exponential. Exponential growth in bacteria involves a doubling (or increase by a certain factor), not a fixed increase, and results in a J-shaped curve when plotted over time.
Explanation:The situation presented in the question, where a population of bacteria increases by 30 every hour, represents a linear function. This is because the function increases by a constant amount. So, the answer is D. Linear, because the function increases by a constant amount. The given scenario differs from an example of exponential growth typically seen in bacteria. In exponential growth, the population of bacteria would double (or increase by a certain factor) each hour as opposed to increasing by a fixed amount. Exponential growth in bacteria occurs when there is an unlimited supply of nutrients, and the population size, when plotted over time, results in a J-shaped growth curve. Here, the rate of increase itself increases with time. In contrast, the linear growth described in the question indicates a steady rate of increase.
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An airplane flies 810 km in 1.5 hours. Find the constant of variation.
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{d}istance of 810 km in 1.5 \underline{h}ours}}{d=kh} \\\\\\ \textit{we know that } \begin{cases} h=1.5\\ d=810 \end{cases}\implies 810=k(1.5)\implies \cfrac{810}{1.5}=k\implies 540=k[/tex]
Answer : The value of constant of variation is, 540
Step-by-step explanation :
As we know that,
[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]
That means,
d = s × t
Here,
's' is constant of variation.
Given:
d = distance = 810 km
t = time = 1.5 hr
Now put the values in the above expression, we get:
d = s × t
810 km = s × 1.5 hr
[tex]s=\frac{810km}{1.5hr}=540km/hr[/tex]
Thus, the value of constant of variation is, 540
Solve using elimination
5x+3y=24
-2x-7y=-56
Answer:
Solution point (0,8)
Step-by-step explanation:
Multiply the top equation by 2
2*(5x + 3y = 24) Remove the brackets10x + 6y = 48 You could simplify this but don't.And multiply the bottom equation by 55*(-2x - 7y = -56)-10x - 35y = -280Now add the two equations together.
10x + 6y = 48 -10x -35y = - 280 The xs cancel out-29y = - 232 Divide by - 29y = -232/-29 Do the division y = 8=================
Solve for x
5x + 3y = 24 Substitute for y5x + 3*8 = 24 Combine on the left5x + 24 = 24 Subtract 24 from both sides 5x = 0 Divide by 5x = 0==================
This one is just a bit messier. I made a graph of it just to show that the answer is correct.
Bailey has an hour to get ready for school he spends 3/6of that time getting dressed she spends 1/4of that time eating breakfast Bailey spend more time getting a dress or eating breakfast
Final answer:
Bailey spends more time getting dressed, which is 1/2 of an hour (30 minutes), whereas she spends 1/4 of an hour (15 minutes) eating breakfast.
Explanation:
The question is asking which activity Bailey spends more time on in the morning: getting dressed or eating breakfast. Since Bailey has an hour to get ready, 3/6 of an hour is spent getting dressed, and 1/4 of an hour is spent eating breakfast.
First, we simplify the fraction for getting dressed, as 3/6 can be reduced to 1/2. Thus Bailey spends 1/2 hour or 30 minutes getting dressed. To find how much time is spent eating breakfast, we calculate 1/4 of an hour, which is 15 minutes.
Comparing the two, we see that Bailey spends more time getting dressed (30 minutes) than eating breakfast (15 minutes).
divisibility rule for 4.
Answer:
Divisable by 4? look at the last two digets If divide by 4, the whole number divides by 4.
4 = 2^2, so if you can divide a number by 2 twice, then the number is divisible by 4.
Find the distance between the points (5/2,3) and (3/2,8)
Answer:
d = [tex]\sqrt{26}[/tex] ≈ 5.1 ( to 1 dec. place )
Step-by-step explanation:
to calculate the distance d use the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = ([tex]\frac{5}{2}[/tex], 3) and (x₂, y₂ ) = ([tex]\frac{3}{2}[/tex], 8)
d =√ ([tex]\frac{3}{2}[/tex] - [tex]\frac{5}{2}[/tex])² - (8 - 3)²
=[tex]\sqrt{1+25}[/tex] = [tex]\sqrt{26}[/tex] ≈ 5.1
Sandra bought a new coat for $49.99 and 3 skirts for $24.99 each . If the Sale tax rate is 7% to the nearest cent what is the amount of sale tax Sandra will owe on the purchase?
The solution is $ 8.75
The sales tax amount Sandra will owe on the purchase is $ 8.75
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the price of the coat be = $ 49.99
Let the price of one skirt be = $ 24.99
The sales tax percentage of Sandra's purchase = 7 %
So , the price of 3 skirts = 3 x price of one skirt
Substituting the values in the equation , we get
The price of 3 skirts = 3 x 24.99
The price of 3 skirts = $ 74.97
Now , the total price of the purchase of Sandra = price of the coat + price of 3 skirts
Substituting the values in the equation , we get
The total price of the purchase of Sandra = $ 49.99 + $ 74.97
The total price of the purchase of Sandra = $ 124.96
And , the sales tax amount of the purchase by Sandra A = sales tax percentage of Sandra's purchase x total price of the purchase of Sandra
The sales tax amount of the purchase by Sandra A = ( 7/100 ) x 124.96
The sales tax amount of the purchase by Sandra A = 0.07 x 124.96
The sales tax amount of the purchase by Sandra A = $ 8.7472
Therefore , the value of A is $ 8.75
Hence , the sales tax amount of the purchase by Sandra is $ 8.75
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Nala has 5,000 customers now she has 100 how many customers did she went away
Nala had lost 4,900 of her customers.
Hope this helps!
Answer:
Nala served 4,900 customers.
Step-by-step explanation:
5,000 to 100
5,000-100=4,900
YaY!!! u got it!!!! =)
a cylinder has a volume of 72 inches. what is the volume of a cone with the same height and radius as the cylinder? Explain
The formula of a volume os a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - heihgt
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
If a cylinder and a cone have the same radius and height then the volume of a cone is three times smaller than a volume of a cylinder.
Therefore
[tex]V_{cone}=\dfrac{1}{3}V_{cylinder}[/tex]
We have
[tex]V_{cylinder}=72\ in^3[/tex]
Substitute:
[tex]V_{cone}=\dfrac{1}{3}\cdot72=24\ in^3[/tex]
Answer: The volume of a cone is 24 in³.Which of the following three dimensional objects has rotational symmetry about a line
Answer:
equilateral triangle, kite, regular pentagon, regular hexagon
a hexagon has rotational symmetry. Furthermore, the angle of rotation is 60° and since there are six copies of 60° in 360° (360 ÷ 60 = 6), we have that the order of rotation of a regular hexagon is six.
let me know if none of these r choices on ur test i will give u more examples :)
Answer:c rolling pin
Step-by-step explanation:
1. c reflectional and point
2. a reflectional
3. d.reflectional, rotational and point
4. c. rolling pin
5. c 10
Can someone plz help me with number 9
Answer:
b
Step-by-step explanation:
b dont want to explain...
Answer:
B would be your correct answer here because you are counting down by negative hope this helps
Step-by-step explan
125 is 500% of what number
let's say that number is "x", so "x" is then the 100%.
we know 125 is the 500%, and "x" is the 100, what is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 125&500 \end{array}\implies \cfrac{x}{125}=\cfrac{100}{500}\implies \cfrac{x}{125}=\cfrac{1}{5} \\\\\\ 5x=125\implies x=\cfrac{125}{5}\implies x=25[/tex]