Answer:
60 miles
Step-by-step explanation:
miles that Sophia drove = 3/5 x 100 = 60 miles
A fraction is a way to describe a part of a whole. The distance covered by Sophia and Toby is 300 miles and 200 miles, respectively.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
A fraction can also be described in the form of a percentages, to represent the part of the whole.
Given that the length of the entire trip is 500 miles. Also, the first 3/5 of the trip are covered by Sophia and the last 2/5 of the trip are covered by Toby.
Now, the distance covered by Sophia and Toby will be,
Distance covered by Sophia = (3/5) × 500 miles = 300 miles
Distance covered by Toby = (2/5) × 500 miles = 200 miles
Hence, the distance covered by Sophia and Toby is 300 miles and 200 miles, respectively.
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Find the probability that a person is male given that the person prefers hiking near lakes and streams. Let M= male and L= prefers lakes and streams.
This is a conditional probability. What word signals that it is a conditional?
Regarding conditional probabilities, the keyword is always given, as a previous event is considered to have happened.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.The previous event having happened is represented by keyword given.
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A linear function contains these points: (0,-1) & (3,8)
What is the slope and y-intercept of this function?
Answer:
slope: 3
y-intercept: (0, -1)
Find slope:
[tex]\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here given points are: (0, -1), (3, 8)
[tex]\rightarrow \sf slope : \dfrac{8-(-1)}{3-0} = \dfrac{9}{3} = 3[/tex]
When finding y-intercept, the value of x is 0. Here given y is -1 when x is 0.
y-intercept: -1 or (0, -1)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
If a linear function contains these points: (0,-1) and (3,8), what is its slope and y-int.?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Formula utilised, here [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].
Put in the values,
[tex]\bf{\dfrac{8-(-1)}{3-0}}[/tex] | subtract on top and bottom
[tex]\bf{\dfrac{9}{3}}[/tex] | divide on top and bottom
[tex]\bf{3}[/tex]
The y-intercept is the second co-ordinate of the point (0,-1)
[tex]\bf{Which\;is\;-1}[/tex].
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{\begin{cases} \bf{Slope=3} \\ \bf{Y-int. -1} \end{cases}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1 \theta l}}[/tex]
I will give BRAINLIEST! ANSWER FOR 30 Points !!!!
Pleasee look at picture
What is the frequency of the tangent function represented in the graph below?
Answer CHOICES:
1 , 4 , 3 , 2
Answer:
The answer is 3
Step-by-step explanation:
You can see that it recurs faster than usual for a tan curve so 1 is eliminated and it cant be 2 or 4 because it isnt recurring equally.
Please give brainliestWhat's the circumference of a
circle with a radius of 7 feet?
Use 3.14 for .
C = [?] feet
Enter the number that belongs in the green
box. Do not round your answer.
Hint: C = 2πr
Answer:
43.96ft
Step-by-step explanation:
In the hint, you are given the equation [tex]C = 2\pi r[/tex].
Here, [tex]C[/tex] is the circumference, [tex]r[/tex] is the radius, and [tex]\pi[/tex] is a constant (a value that doesn't change). In this question, you are told to assume the value of [tex]\pi[/tex] is 3.14.
You are told the radius is 7, therefore, [tex]r[/tex] = 7.
Now we have these values, let's substitute them into the equation:
[tex]C = 2 * 3.14 *7[/tex]
For clarification, the stars mean multiplication.
So, the product of those values will give us our circumference, [tex]C[/tex].
In this case, you get an answer of 43.96ft.
Find the smallest number such that
when divided by 18, the remainder
is 17, when divided by 20 the
remainder is 19 and when divided
by 24, the remainder is 23.
Answer:
I think the answer is 7
don't blame me if I'm wrong
Answer:
359
Step-by-step explanation:
the prime factors of the numbers are
18 = 2×3×3
20 = 2×2×5
24 = 2×2×2×3
the lowest common multiple is therefore
2×2×2×3×3×5 = 360
the difference between the checked divisor numbers and the expected remainder is constantly 1 :
18 - 17 = 1
20 - 19 = 1
24 - 23 = 1
so, we can deduct this constant 1 from the LCM and get the desired number :
360 - 1 = 359
verify :
359 ÷ 18 = 19 remainder 17
359 ÷ 20 = 17 remainder 19
359 ÷ 24 = 14 remainder 23
The number N of tree of a given species per acre is approximated by the model
N = 68(10)-0.042
above the ground.
Use the model to approximate the average diameter of the trees in a test plot when N = 21.
7,5 ≤ x ≤ 40 where x is the average diameter of the trees (in inches) 3 feet
Answer:
1 answer
The area of triangle with vertices A(0, 9), B(0, 4) and C( - 5, - 9) is
what is the equation of the following line? be sure to scroll down first to see all the answer options
E. y = -3x
I can give you an explanation in the comments if you'd like
Simplify x^2+2x+1 divided by x+1
The quotient is x+1.
What Long division method?Long division is a method for dividing one large multi digit number into another large multi digit number.
Given:
f(x)= x²+2x+1
g(x)= x+1
The steps to divide the polynomial is :
Divide the leading term of the dividend by the leading term of the divisor: x²/x=x.Multiply it by the divisor: x(x+1)=x²+x.Subtract the dividend from the obtained result: (x²+2x+1)−(x²+x)=x+1.Divide the leading term of the obtained remainder by the leading term of the divisor: x/x=1.Multiply it by the divisor: 1(x+1)=x+1.Subtract the remainder from the obtained result: (x+1)−(x+1)Learn more about long division method here:
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I opened a grocery account at my bank with $100. Every week thereafter, I withdraw $45 from the account to pay for groceries. If x is the number of weeks I've had the account, then y is the amount in the account. Find an equation of a line in the form y = mx + b that describes my grocery account balance.
Answer:
y=-45x + 100
Step-by-step explanation:
The slope-intercept form is y=mx+b where m is the slope and b is the y-intercept or in other words the initial amount (when x is 0). Since you start off with 100 dollars the y-intercept is going to be 100 since after 0 weeks (when you opened the account) you put 100 dollars in... so you should have 100 dollars. The slope is going to be -45 since you are withdrawing 45 each week so the value is going to be decreasing by 45 every week. If you put that together you get y=-45x+100
again with this please
Answer:
a) A dozen= 24
3 dozen= 24 x 3
= 72
b) 1 dozen= 12 bananas
A dozen cost= 24
So, 1 banana cost= 24/12
= 2
So, 6 bananas would be 2 x 6 = 12
c) 1 dozen= 12 bananas
A dozen cost= 24
1 banana cost= 24/12
= 2
d) I need to know how many people are there in your class so please mention that first :)
Mark me brainliest pleaseee
A football teams offense T is found by adding the total passing yardage P to the total rushing yardage R; that is, T=P+R. During the 2012 regular football season, the teams total offense was 4559 yards. The teams passing yardage was 3069 yards. How many yards did the team gain by rushing during the season?
The team gain 1490 yards by rushing during the season.
What is football yardage?Football yardage is the number of yards that a team or player manages to move the ball forward toward their opponent's end zone.
According to the question,
A football teams offense T is found by adding the total passing yardage P to the total rushing yardage R,
i.e. T=P+R
In 2012,
The teams total offense was 4559 yards.
The teams passing yardage was 3069 yards.
By using the formula
T=P+R
T = 4559 yards , P = 3069 yards
Put the values in the above equation;
4559 = 3069 - R
4559 - 3069 = R
R = 1490 yards
Therefore , 1490 yards the team gain rushing during the season.
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A 20-ft by the 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 256 ft2, how wide is the walkway?
========================================================
Explanation:
x = width of the walkway in feet
This is some positive real number.
The dimension of 20 feet bumps up to 20+2x when adding on x from both directions. Similarly, the 40 ft dimension becomes 40+2x
Refer to the diagram below.
The 20 ft by 40 ft pool is surrounded by a larger rectangle that is 20+2x ft by 40+2x ft
The pool itself is 20*40 = 800 sq ft. Add on the walkway area to get 800+256 = 1056 sq ft.
-----------
Area = length*width
1056 = (20+2x)*(40+2x)
1056 = 20*40 + 20*2x + 2x*40 + 2x*2x ... FOIL rule
1056 = 800 + 40x + 80x + 4x^2
0 = 4x^2 + 40x + 80x + 800 - 1056
0 = 4x^2 + 120x - 256
4x^2 + 120x - 256 = 0
4(x^2 + 30x - 64) = 0
x^2 + 30x - 64 = 0
Let's use the quadratic formula to finish solving for x.
Plug in a = 1, b = 30, c = -64
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-30\pm\sqrt{(30)^2-4(1)(-64)}}{2(1)}\\\\x = \frac{-30\pm\sqrt{1156}}{2}\\\\x = \frac{-30\pm34}{2}\\\\x = \frac{-30+34}{2} \ \text{ or } \ x = \frac{-30-34}{2}\\\\x = \frac{4}{2} \ \text{ or } \ x = \frac{-64}{2}\\\\x = 2 \ \text{ or } \ x = -32\\\\[/tex]
Recall we made x be positive. This is because a negative walkway width does not make sense. This means we'll ignore x = -32.
The only practical solution is x = 2
Therefore, the walkway is 2 feet wide
Need help, can't figure this one out:
Find the perimeter of the following rectilinear figure.
The perimeter of the following rectilinear figure is 54 units.
What is Perimeter ?Perimeter of a figure is the distance covered when a person walk one round across its edges .
The given figure is in the form of a rectangle ,
The perimeter is equal to the sum of all sides ,
The bottom base is 13 includes (base of the small extended figure )
The left side is 14(includes left side of the small extended figure)
The right side is 10+5+4 (includes right side of the small extended figure)
The top is 8
Therefore the perimeter is 13+14+10+5+4+8 = 54 units
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A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 90% confident that his estimate is in error by no more than two percentage points
Answer:
The number of computers that must be surveyed is 1681.
Step-by-step explanation:
The formula to find the sample size is given by:-
[tex]n=p(1-p)(\frac{\frac{z_{\alpha } }{2} }{E} )^{2}[/tex]
where p = prior population proportion,
[tex]\frac{z_{\alpha }}{2}[/tex]= Two-tailed z-value for ∝
E= Margin of error.
As per the given, we have
Confidence level :
1 - ∝ = 0.90
⇒∝= 1 - 0.90= 0.10
Two -tailed z-value for ∝= 0.10 : [tex]\frac{z_{\alpha }}{2}[/tex] = 1.64
E= 2%=0.02
We assume that nothing is known about the percentage of computers with new operating systems.
Let us take p=0.5 [we take p= 0.5 if the prior estimate of proportion is unknown.]
The required sample size will be:-
[tex]n= 0.5(1-0.5)(\frac{1.64}{0.02} )^{2}[/tex]
=> [tex]0.25(82)^{2}[/tex]
=> 1681
Hence, the number of the computer must be surveyed = 1681
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a farmer uses 1/6 of his land to plant pineapples, 5/9 to plant durians and the remaining 48.5 acres to plant vegetables. calculate the area of land used to plant pineapples and durians
Step-by-step explanation:
x = total area of land
x - 1/6 × x - 5/9 × x = 48.5 | multiply both sides by 6
6x - x - 30/9 × x = 291
5x - 30/9 × x = 291 | multitude both sides by 9
45x - 30x = 2,619
15x = 2,619
x = 174.6 acres
pineapples were planted on 174.6 × 1/6 = 29.1 acres.
durians were planted on 174.6 × 5/9 = 97 acres.
Evaluate the expression.
-2(12 - 2 (-4))²
What is the value of the expression?
Enter your answer in the box.
Answer:
-2(10(-4))²
-2(-40)²
-2 × 1600
= -3200
Answer: = -3200
Step-by-step explanation:
took the test
Gianna used two refrigerators, each set to a different temperature, to cool two cups of hot liquid.
She placed the first cup in refrigerator A. The temperature, in degrees Fahrenheit, of the liquid in this cup, after x minutes in the refrigerator, is represented by the graphed function.She placed the second cup in refrigerator B. The temperature, in degrees Fahrenheit, of the liquid in this cup is represented by an exponential function that has a y-intercept of 96 and approaches 38 as x increases.
The answers are
1). warmer
2). higher
3). end behavior
What is Refrigerator?
A refrigerator is a device which is designed to remove heat from a space that is at lower temperature than its surroundings.
When Gianna initially placed the two cups in the refrigerators, the liquid placed in refrigerator A was warmer than the liquid placed in refrigerator B.
The end behavior of the two functions implies that refrigerator A is set to a higher temperature than refrigerator B.
The graph for the question given below.
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Find the area.
help pls
Answer:
30 square feet
Step-by-step explanation:
The area of a trapezoid is equal to (a+b)/2 * h
In this case, the value of a is 5, b is 10, and h is 4. You can substitute those numbers into the formula and get the answer of 30.
If f(x) = 3x + 2 what is f(5)?
Answer:
f(1)= 3×1 + 2 = 5
....
.....
....
f(5)= 3×5 + 2 = 17
Answer:
f(5) = 17
Step-by-step explanation:
Given: f(x) = 3x + 2
We are asked to find the value of the function when the value of x is 5
Substitute 5 as the value of x in the function:
⇒ f(x) = 3x + 2
⇒ f(5) = 3(5) + 2 [multiply]
⇒ f(5) = 15 + 2 [add]
⇒ f(5) = 17
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what is the value of n in the equation -1/2(2n +4) + 6 = -9 + 4 (2n +1)
Answer:
n=1
Step-by-step explanation:
-n+4=8n-5
9=9n
n=1
hope that helps
Could someone answer the rest please!
Much appreciated if you do (:
Answer:
shown below
Step-by-step explanation:
4 x 2 = 8
1 x 2 = 2
a⁸b²
(a⁵b²)(a²b⁶)
a⁷a⁵b⁶b²a²b⁸
a¹⁴b¹⁶
8 - 14 = -6
2 - 16 = -14
a^-6 b^-14
next one
25^3x-21
/
25^2x+14
1^x-35
Item at position 9
The lifetimes of 20,000 light bulbs are normally distributed. The mean lifetime is 230 days. The standard deviation is 40 days. Find the values defined by standard deviation in a normal distribution for 3 standard deviations.
Using the normal distribution, the values within 3 standard deviations of the mean are given 110 to 350.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 230, \sigma = 40[/tex].
The bounds of the values within 3 standard deviations of the mean are given by X when Z = -3 and X when Z = 3, hence:
Z = -3:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-3 = \frac{X - 230}{40}[/tex]
X - 230 = -3(40)
X = 110.
Z = 3:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]3 = \frac{X - 230}{40}[/tex]
X - 230 = 3(40)
X = 350.
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pls someone help me asap
Answer:
Area: 15.53 square inches
Perimeter: 15.71 inches
Step-by-step explanation:
Area:
So the area of the rectangle is pretty easy to find and is just the width * height. In this case it's 4 * 3 which is 12. Now the area of a circle is [tex]\pi r^2[/tex]. But since this is a semi circle it's half of that which is [tex]\frac{\pi r^2}{2}[/tex]. The diameter of the semicircle is 3 as it sits on top of the rectangle. The radius is half of the diameter so the radius is 1.5. Now plug that into the equation and you get [tex]\frac{(3.14) (1.5)^2}{2} = 3.5325[/tex]. Now add that to 12 and you get 15.5325. Round that number to the nearest hundredth and you get 15.53. So that's the area.
Perimeter:
Pi is the ratio of any circle's circumference to the diameter. Or in other words the circumference is equal to the diameter * 3.14. The diameter is 3 which you multiply by 3.14 to get the circumference of a circle. This will get you 9.42 but since it's a semicircle, the circumference is half of this value which is 4.71. The perimeter of the rectangle is just 2 times the width + 2 times the height. This is not completely the case in this shape since one of the sides of the rectangle is not a side of the two shapes joined together. Which is the side that is parallel to the side of length 3 inches. So the perimeter is going to be 2(4) + 3. This gives you 11 which you add to the 4.71 and get 15.71
In pqr the measure of r=90 qp=65 rq=33 and pr=56 what ratio represents the sine of q
We can use sine ratio in given right angled triangle.
The sine of ∠Q is represented by ratio 48/73.
Given data:
∠R=90°,
QP = 73,
PR = 48,
RQ = 55
We know that;
The sine of a given angle in a right angle triangle is the ratio of perpendicular and hypotenuse seen from the viewpoint of that angle.
Since, against ∠Q lies the side PR, thus, PR is perpendicular. The side PQ is hypotenuse.
Thus, we have:
sin Q = PR/PQ
= 48/73
Thus, the sine of ∠Q is represented by ratio,
48/73.
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Solve for y.
frankly im confusion
a:4.53
b.4
c.7.47
c.8
Answer:
8
Step-by-step explanation:
Due to lines r & s being parallel to each other, we can apply the rule of alternate interior angles to solve for y in this problem.
Applying this, we'll be obtaining the equation that of:
[tex]116=15y-4[/tex]
We now simply solve for y.
[tex]120=15y\\y=8[/tex]
Therefore, y is equal to 8.
This can be checked by plugging it into the equation:
[tex]15(8)-4[/tex]
[tex]120-4[/tex]
[tex]116[/tex]
And look at that, we got 116 for our answer, exactly the same as the other angle.
Any questions feel free to ask :)
need help figuring out the answers
Answer:
3, -1, 1 and 0
Step-by-step explanation:
An expression is undefined when the denominator is equal to 0 as you cannot divide by 0 in Mathematics. Therefore you are looking for the values of x which will result in either or both denominators equaling 0.
This simply means finding the solutions to the quadratics in the denominators.
First equation is [tex]x^{2} -2x-3[/tex].
One way you can solve this equation is using factorization (putting the equation into two sets of brackets which show the solutions) which puts the equation in the solvable form: (ax+b)(cx+d).
Firstly, we can deduct that a and c are both 1 as ax and cx multiply to give the x^2 term, the co-efficient of which is 1. Since only 1 and 1 can multiply to 1, a and c must both be 1.
Now, in order to work out b and d we need to find the possible factor combinations for -3 as b and d multiply to give the constant term. The only possible combination is 1x3, therefore b and d can either be -1 and 3, or -3 and 1.
To work this out we look at the x term. We see it is -2x. b and d will add to give the co-efficient.
Therefore we know that they are -3 and 1 as -3+1 = -2
We now have the equation: (x+1)(x-3)
Setting it to 0 gives us: [tex](x+1)(x-3)=0[/tex]
This tells us the solutions to this equation are x= -1 and x= 3 as substituting these values for x will result in a bracket adding to 0 so both those options can be selected as your answer.
The second equation [tex]2x^{2} +2x[/tex] can be approached with a slightly easier method. Both terms have a 2x, so we can condense it into a bracket by dividing both terms by the common factor and moving the factor outside. Factorizing this equation in this fashion gives us: [tex]2x(x+1)=0[/tex]
Now our solutions are x=0 and x=1.
Combined from both equations the correct options are: 3, -1, 1 and 0.
Hope this helped!
What is 6289 round off to the nearest 1000 (thousand)????
Answer:
6230 will be answer I think
Mark me as Brainliest
Answer:
Well, it's to the nearest thousand, and we know that 6289 is 6 thousand 2 hundred and 89. So, you look at the number next to the thousand which is the hundreds, and as we can see that is 2. Therefore it will be 6000, as 6289 cannot be rounded to 7000 since 2 doesn't exceed 5.
So, the answer is 6000
(I don't mind being marked brainliest for this I'd just like to help someone. :)
What is the degree of the monomial?
8x²y³z4
What are the zeros of the quadratic function f(x)=6x^2+12x-7?
(Please pick from one of the options in the photo)
The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.
The missing options are given below.
What is the solution of the quadratic equation by formula method?The quadratic equation is given as ax² + bx + c = 0.
Then the solution is given as
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic function is given below.
f(x) = 6x² + 12x – 7
Then the zeroes of the quadratic function will be
[tex]\rm x = \dfrac{-12\pm \sqrt{12^2 - 4 * 6 * (-7)}}{2 * 6}\\\\\\\rm x = \dfrac{-12\pm \sqrt{312}}{12}\\\\\\\rm x = -1 \pm \sqrt{\dfrac{13}{6}}\\\\\\x = -1 - \sqrt{\dfrac{13}{6}} , -1 + \sqrt{\dfrac{13}{6}}[/tex]
Then the correct option is A.
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Question 4(Multiple Choice Worth 4 points)
Which of the following is a rational number?
√1. √2. √3, √5
O√1
O √2
O√3
√√5
Answer:
[tex]\sqrt{1}[/tex]
Step-by-step explanation:
We know that a rational number cannot have roots. All of the answer choices cannot be simplified except for [tex]\sqrt{1}[/tex], which can become 1. Therefore, our answer is [tex]\sqrt{1}[/tex].
