Answer:
Julie's score is 15.
Step-by-step explanation:
This can be solved in two ways:
⇒ 120 ÷ 8
⇒ Experimentation on what × 8 = 120 (adding random numbers until you get 120 as a product).
Let's use the first method.
⇒ 120 ÷ 8
1 5
__________
8 | 1 2 0
- 8
____
4 0
- 4 0
____
0
Therefore, Julie's score is 15.
Work out the angle of elevation from the
rabbit to the top of the tree.
18 m
9√3m
Not drawn accurately
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Angle \:\: of \:\: elevation= 30° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Let the angle of elevation be " x "
[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{9 \sqrt{3} }{18} [/tex]
[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{ \sqrt{3} }{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = \cos {}^{ - 1} \bigg( \cfrac{ \sqrt{3} }{2} \bigg ) [/tex]
[tex]\qquad \tt \rightarrow \: x = 30 \degree \: \: or \: \: \cfrac{ \pi}{6} \: \: rad[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
The angle is 60 degree.
Step-by-step explanation:
First of all, we will find the height if the tree by using Pythagorean theorm.
Let, height of tree be x.
18^2=(9(3^1/2))^2+x^2
324=243+x^2
x^2=324-243
x^2=81
x=9
Now, let the angle be y.
tan y= x/base
tan y=9/9×(3^1/2)
tan y=1.73
y=cot 1.73
y= 60
Lyanna opens a bank account with a deposit of $200. She earns 3%
interest per year. How much money will Lyanna have in her account after
the first year?
Answer:
$206
Step-by-step explanation:
Lyanna will earn 3% on her capital within 1 year.
In total, she will have 103%.
$200 x 103% = $206
The marketing manager of a cell-phone company wants to determine which cell phone model most of her customers prefer. She separates a list of her customers into three age groups and then randomly selects a sample from each group proportional to the number of customers in each group.
What sampling method did she use?
A. Simple random sampling
B. Stratified random sampling
C. Systematic random sampling
D. Non-random sampling
Answer:
C
Step-by-step explanation:
I guess it is the answer because the manager separates the customers into 3 ange groups and randomly selects a sample from each group
Answer:
B. Stratified random sampling
Step-by-step explanation:
In a stadium, 1,000 tickets were sold. Children’s tickets cost $2.50 each and adults’ tickets cost $5.00 each. The revenue collected for the game was $4,000. How many children’s tickets were sold? How many adults’ tickets were sold?
Answer:
400 children tickets and 600 adult tickets.
Step-by-step explanation:
children tickets in total cost=400x2.50
=1000
adult tickets in total cost=600x5.00
=3000
total cost is 4000
there were 3 parts to Ritas race she ran the first part which was 4/9 of the total distance, in 20 minutes she ran the second part which was 2/5 of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at the speed of 300 meters per minute.
How long was the first part of the race? What was Ritas speed in that section of the race?
Answer:
3/5 .................................. 6/9
Step-by-s4tep explanation:
Answer:
300 meters per minute
Step-by-step explanation:
Step 1
Determine the fraction of the total distance for each part of the race.
Given:
1st part of race = 4/9 of total distance2nd part of race = 2/5 of remaining distance[tex]\begin{aligned} \implies \sf 2nd\:part & = \sf \dfrac{2}{5}\:of\:remaining\:distance\\ & = \sf \dfrac{2}{5} \times\left(1-\dfrac{4}{9}\right)\\& = \sf \dfrac{2}{9}\:of\:total\:distance\end{aligned}[/tex]
[tex]\begin{aligned}\implies \sf 3rd\:part & = \sf 1-1st\:part-2nd\:part\\& = \sf 1-\dfrac{4}{9}-\dfrac{2}{9}\\& = \sf \dfrac{1}{3}\:of\:total\:distance\end{aligned}[/tex]
Step 2
Determine the distance of the third part of the race.
Given:
time = 15 minutesspeed = 300 meters per minute[tex]\begin{aligned}\sf Distance & = \sf speed \times time\\& = \sf 300 \times 15\\& = \sf 4500 \:\:meters\end{aligned}[/tex]
Step 3
If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:
[tex]\begin{aligned} \sf Total\:distance & = \sf 4500 \times 3\\& = \sf 13500\:meters \end{aligned}[/tex]
Step 4
Determine the distance of the 1st part of the race:
[tex]\begin{aligned}\sf Distance\:of\:1st\:part\:of\:race & = \sf \dfrac{4}{9} \:of\:total\:distance\\& = \sf \dfrac{4}{9} \times 13500\\& = \sf 6000\:meters \end{aligned}[/tex]
Step 5
Determine the speed of the 1st part of the race:
Given:
time = 20 minutesdistance = 6000 m[tex]\begin{aligned}\sf Speed\:of\:1st\:part\:of\:race & = \sf \dfrac{distance}{time}\\& = \sf \dfrac{6000}{20}\\ & = \sf 300\:meters\:per\:minute\end{aligned}[/tex]
A financial planner has three portfolios: A, B, and C. Because investors have different tolerances for risks, 35% of people are likely to invest in portfolio A, 25% are likely to invest in B, and 40% are likely to invest in C. Each portfolio has both stocks and bonds, and investors are equally likely to choose either.
This is a tree diagram that represents the probability of investors choosing the different financial products.
What is the probability of an investor choosing both stocks AND bonds from portfolio B?
The probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
A financial planner has three portfolios: A, B, and C.
Each portfolio has stocks and Bond
P(stock) = 0.5
P(bond) = 0.5
Customers are equally likely to choose stocks.
P(stock and bond from B) = P(stock, B) + P(bond, B)
= 0.25×0.5 + 0.25×0.5
= 0.25 or
= 25%
Thus, the probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.
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What are the solution(s) to the quadratic equation 9x² = 4?
0 x =
and x =
0 x =
I
69
4
and x = -
2
0 x = ² and x = -²
2
Ono real solution
Answer:
x= 2/3, -2/3
Step-by-step explanation:
9x² = 4
To solve this quadratic, divide each side by 9
x^2 = 4/9
Take the square root of each side
sqrt(x^2) = sqrt(4/9)
x = ±2/3
Answer:
x = ± [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
9x² = 4 ( divide both sides by 9 )
x² = [tex]\frac{4}{9}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{4}{9} }[/tex] = ± [tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex] = ± [tex]\frac{2}{3}[/tex]
x = - [tex]\frac{2}{3}[/tex] , x = [tex]\frac{2}{3}[/tex]
A container is an open cylinder whose height and radius are of equal length. The total surface area of the container is 300 cm³. Find the radius of the container.
Answer:
The radius of the container is approximately 4.89 cm
Step-by-step explanation:
GivenA container with:
r = hS = 300 cm²To findThe radius of the containerSolutionUse the equation for total surface area of cylinder:
S = 2πr² + 2πrh or S = 2πr(r + h)Since we have r = h and the value of S is known, let's solve this equation:
2πr(r + h) = 3002πr(r + r) = 3002πr(2r) = 3004πr² = 300πr² = 753.14r² = 75r² = 75/3.14r² = 23.89 (rounded)r = √23.89r = 4.89 cm (rounded)53 points!!! find x. do not round your answer. 5cm 6cm 12cm x
Answer:
16.6
Step-by-step explanation:
By the property of intersecting secants.5(5+x) = 6(6+12)-> 25 + 5x = 6*18-> 5x = 108 - 25-> 5x = 83-> x = 83/5-> x = 16.6There is a bag filled with 6 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?
Answer:
1/11
Step-by-step explanation:
probability =total number of items ÷ 1
=11÷1
=1/11
question 10 please
need help
Answer:
Denes Dynamos =
2012 attendance = 34500
2013 attendance = 30705
change = 30705 - 34500= -3795
change percentage = -3795 * 100 / 34500 = -11%
Edgefield Eagles =
2012 = 24100
2013 = 21208
change = -2892
change Percentage = -2892 * 100 / 24100 = -12%
how much is 20 Pepsi if one Pepsi is sold at the rate of 20 naira
Answer:
Let x= cost of 20 pepsi
so 1 Pepsi = 20 naira
20 = x
x= 20*20
x= 400 naira
Therefore the cost of 20 pepsi is 400 naira
Need help please. Math and I'll give 30 points. Please and thank you. :D
And have a great day! :)
Answer:
h = 17.5 m
Step-by-step explanation:
We have 2 similar right triangles as models of the situation
one has legs with George's height and shadow
the other is the height h of the tree and length of it's shadow
the corresponding sides of the 2 triangles are in proportion, that is
[tex]\frac{6.25}{h}[/tex] = [tex]\frac{10}{28}[/tex] ( cross- multiply )
10h = 175 ( divide both sides by 10 )
h = 17.5 m
Convert 203 yards into meters.
Hint: 1 yard=0.91 meters
203 yards=[blank]−−−−−− meters
Enter your answer as a number that correctly fills in the blank.
Round the answer to two decimal places, like this: 45.53
Answer:
184.73
Step-by-step explanation:
1 yard = 0.91m
203 yard=?
(203x0.91)/1=184.73.
+1(415) 450-6164
Find the surface area for the rectangular prism below.
Please answer with steps! :)
If f(x)=2x² +5√(x-2), complete the following statement:
The domain for f(x) is all real numbers ____ than or equal to 2.
Free Response:
By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.
How to determine the domain of a function with radical components
Domain is the set of x-values such that the value of the function exists. By algebra we know that the domain of polynomials is the set of all real numbers, whereas the domain of radical functions is the set of x-values such that y ≥ 0. If we know that f(x) = 2 · x² + 5 · √(x - 2), then the domain is restricted by the radical component and defined by x ≥ 2.
By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.
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WILL MARK BRAINLIEST!!! According to the synthetic division below, which of the following statements are true? Check all that apply.
According to the given synthetic division, the statements that are true are; Options A, C and E
How to carry out Synthetic Division?
In the synthetic calculation we use the coefficient of the dividend
with the factors of the function.
Therefore;
3 , -13 , 4 are the coefficient of the dividend 3x² - 13x + 4
Therefore, the divisor is 4 and as such x = 4 is a root of f(x) = 3x² - 13x + 4
Also, it means that (x - 4) is a factor of the dividend F(x) = 2x² - 2x - 12
- The quotient is the last line of the synthetic division. Thus, the coefficients of quotient are 3, -1.
- The quotient is 1 degree less than the dividend and so the degree of the dividend is 2.
- The degree of the quotient is 1 and so the he quotient is 3x - 1.
Thus, options A, C and E are correct
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Determine the measure of angle BFE 1 ) 69 degrees 2 ) 112 degrees 3 ) 11 degrees 4 ) 224 degrees
Answer:
option 2
Step-by-step explanation:
the chord- chord angle BFE is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
∠ BFE = [tex]\frac{1}{2}[/tex] ( BE + DC) = [tex]\frac{1}{2}[/tex] (72 + 152)° = [tex]\frac{1}{2}[/tex] × 224° = 112°
which expression is equivalent to 354x + 332, If x=0?
Answer:
10x + 332
when, x=0
Step-by-step explanation:
Please give me brainlist.
The average daily high temperature in [tex] ^{\circ}C[/tex] in Karachi, Pakistan, on the [tex]t^{\text{th}}[/tex] day of the year is approximately
[tex]\qquad T(t) = 29 - 5\cos\left(\dfrac{2\pi (t- 12)}{365}\right)[/tex]
What are the highest and lowest average daily highs in Karachi? Give exact answers.
[tex]\rule{250pt}{2pt}[/tex]
Please explain it "thoroughly" in 'sentences' and with mathematical expression how exactly you'd figure out the answer. I know the answer. I need an elaborate explanation of the method. It's an imperative part of the question to explain your answer otherwise your answer would be considered incomplete
Giving 25 points, thanks (both in your answer and profile)!5 stars and of course brainliest!!!
Given expression
[tex]\\ \rm\Rrightarrow T(t)=29-5cos\left(\cfrac{2\pi (t-12)}{365}\right)[/tex]
Now
We know according to property of cosine function
It has range of [-1,1] for all intervals .This property is enough for our calculations
Let's check
As t represents no of days hence it can't be negative
t must be a whole number set memberSo
for positive interval
We shall use the cosine interval [0,π]We know that
cosπ is -1cos0=1Hence it's enough for our range [-1,1]
Now
In the expression
29 is the vertical shiftLet
[tex]\sf cos\left(\cfrac{2\pi(t-12)}{365}\right)=n[/tex]
Substitute n for lowest and highest value of range
When n=-1
[tex]\\ \rm\Rrightarrow T(\pi)=29-5(-1)=29+5=34°C[/tex]
When n=1
[tex]\\ \rm\Rrightarrow T(0)=29-5(1)=29-5=24°C[/tex]
Highest average daily high=34°Clowest average daily high=24°CAnswer:
Highest temperature: 34°C
Lowest temperature: 24°C
Explanation:
In a Normal Trigonometry Function: y = A + B sin(x) or y = A + B cos(x)
Maximum value: A + |B|
Minimum value: A - |B|
In this trigonometric function, A = 29, B = -5
Hence find minimum/maximum:
Maximum value: A + |B| = 29 + |-5| = 34
Minimum value: A - |B| = 29 - |-5| = 24
Hence, the maximum/highest temperature is 34°C and minimum/lowest temperature is 24°C in Karachi, Pakistan.
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help its timed 12 pts
Answer:
A
Step-by-step explanation:
I think your right!
Answer:
B
Step-by-step explanation:
I think it means the roots, at which the line crosses the x-axis, in which case, the answer is B, 0 and 1.4
find the value of x
Answer:
1 = 120
2 = 120
Step-by-step explanation:
In your research study measuring the relationship between time spent playing video games and course grades, you find that grades increase at about the same rate as time spent playing video games decreases. What do you conclude
Research study measuring relationship suggests that video games may have a detrimental effect on an individual's grades.
This study analyzes the correlation between video game usage and academic performance. Scholastic Aptitude Test (SAT) and grade-point average (GPA) scores were used to gauge academic performance. The amount of time a student spends playing video games has a negative correlation with students' GPA and SAT scores. As video game usage increases, GPA and SAT scores decrease.
A chi-squared analysis found a p value for video game usage and GPA was greater than a 95% confidence level (0.005 < p < 0.01). This finding suggests that dependence exists. SAT score and video game usage also returned a p value that was significant (0.01 < p < 0.05). Chi-squared results were not significant when comparing time spent studying and an individual's SAT score. This research suggests that video games may have a detrimental effect on an individual's GPA and possibly on SAT scores. Although these results show statistical dependence, proving cause and effect remains difficult, since SAT scores represent a single test on a given day. The effects of video games maybe be cumulative; however, drawing a conclusion is difficult because SAT scores represent a measure of general knowledge. GPA versus video games is more reliable because both involve a continuous measurement of engaged activity and performance. The connection remains difficult because of the complex nature of student life and academic performance. Also, video game usage may simply be a function of specific personality types and characteristics.
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What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer: Choice D) x is a real number
Reason:
We can replace x with any number we want without any restriction. There's no issues dealing with division by zero errors for instance, and we also don't have negatives under square roots to worry about. The domain of any linear function is always "the set of all real numbers".
Extra info: The domain in interval notation is [tex](-\infty, \infty)[/tex] which could be thought of as [tex]-\infty < x < \infty[/tex], i.e. x is between negative infinity and positive infinity.
Answer:
d
Step-by-step explanation:
answer...............
In the given graph point B is a relative maximum with the coordinates (0, 2).
The given function is [tex]y=x^{4}-2x^{2} +1[/tex].
In the given graph, we need to find which point is a relative maximum.
What are relative maxima?The function's graph makes it simple to spot relative maxima. It is the pivotal point in the function's graph. Relative maxima are locations where the function's graph shifts from increasing to decreasing. A point called Relative Maximum is higher than the points to its left and to its right.
In the graph, the maximum point is (0, 2).
Therefore, in the given graph point B is a relative maximum with the coordinates (0, 2).
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which equation matches this graph?
The first function represents the graph of a function provided in the picture option first is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a graph of a function shown in the picture.
[tex]\rm f\left(x\right)\ =\ -\sqrt{\left(x-3\right)}\ +\ 2[/tex]
x - 3 ≥ 0
x ≥ 3
Plug x = 3
f(x) = 2
Thus, the first function represents the graph of a function provided in the picture option first is correct.
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What are the features of the quadratic function f(x)=(x-3)(x+7)?
Answer:
It's vertex (-2,-25)x-intercept x₁=-7,x₂=3y-intercept f(0)=-21domain,xER or x is an element of real numberit's neither even nor odd functionA car manufacturer has parked some new cars in 2 car parks.In the first car park there are 60 cars in the ratio 1 red car for every 2 blue cars and 3 silver cars.In the second car park there are 80 cars in the ratio 2 blue cars for every 3 red cars and 5 silver cars.
11. How many red cars are there altogether?
12.How many blue cars are there altogether?
13.How many silver cars are there together?
The total number of red cars is 34, the total number of blue cars is 36, and the total number of silver cars is 70.
How do we solve ratio problems?
The ratio problems can be solved as follows:
11. The total number of red cars can be calculated as follows:
Number of red car in the first car park = (1 / (1 + 2 + 3)) * 60 = 10
Number of red car in the second car park = (3 / (2 + 3 + 5)) * 80 = 24
Total number of red cars = 10 + 24 = 34
12. The total number of blue cars can be calculated as follows:
Number of blue car in the first car park = (2 / (1 + 2 + 3)) * 60 = 20
Number of blue car in the second car park = (2 / (2 + 3 + 5)) * 80 = 16
Total number of blue cars = 20 + 16 = 36
13. The total number of silver cars can be calculated as follows:
Number of silver car in the first car park = (3 / (1 + 2 + 3)) * 60 = 30
Number of silver car in the second car park = (5 / (2 + 3 + 5)) * 80 = 40
Total number of silver cars = 30 + 40 = 70
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1. Identify your variables using let statements.
2. Determine the equations for the linear system.
3. Determine the solution to the linear system (point of intersection)
4. Explain the meaning of the solution using a therefore statement.
Chris is mixing 2 different types of fruit juice together for a summer drink. The two types of juices he is using is one that is 30% strawberry concentrate and the other is 55% lemon concentrate. If he wants 2 L that is 40% concentrate of the fruit juices, how much of each should be used to create the drink?
The meaning of the solution is; Therefore, 1.2 liters of the strawberry concentrate and 0.8 liters of the lemon concentrate.
What is the solution to the system of equations?It follows from the task content that the variables are;
let x be the amount of 30% strawberry concentrate.
let y be the amount of 55% lemon concentrate.
The equations of the linear system according to the task content are as follows;
x + y = 20.30x + 0.55y = (2 ×0.4)From the first equation; x = 2-y;
Hence, upon substitution; we have;
0.30(2-y) + 0.55y = 0.8
0.25y = 0.2.
y = 0.2/0.25 = 0.8L.
Hence, x = 2- 0.8 = 1.2L.
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Kit and Kat are building a kite for the big kite festival. Kit has already
cut his sticks for the diagonals. He wants to position P so that he will
have maximum kite area. He asks Kat for advice. What should Kat
tell him?
Kat should tell Kim that It's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
How to calculate the area of a kite?In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:
A = ½ × d₁ × d₂
Where:
A is the area of a kite.d₁ and d₂ are the length of the diagonals of a kite.Since Kit has already cut his sticks for the diagonals, Kat should tell him that it's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
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