Answer: 1.87 kg of pears
Step-by-step explanation:
7.5 kg of both apples and pears were sold. 3/4 of this 7.5 kg is apples which means the amount of apples sold is:
= 7.5 * 3/4
= 5.63 kg of apples
The amount of pears sold would therefore be:
= Total amount sold - Amount of apples
= 7.5 - 5.63
= 1.87 kg of pears
Please I need help.
Find each length or area to the nearest tenth.
ZY:_____
XZ:_____
Area of XYZ:_____
Answer:
XZ = 26.7
ZY = 11.7
Area = 140.4 sq inches
Step-by-step explanation:
m∠Z = 180-(26+90) = 64°
to get XZ you can use the law of sines:
sin 90°/XZ = sin 64°/24
1/XZ = sin(64°)
cross-multiply to get:
XZ·sin(64°) = 24
XZ = 24/sin(64°)
XZ = 26.7
to get ZY you can use the law of sines again:
sin 64°/24 = sin 26°/ZY
cross-multiply to get:
ZY·sin(64°) = 24·sin(26°)
ZY = 24·sin(26°) ÷ sin(64°)
ZY = 11.7
Area = 1/2(11.7)(24)
= 12(11.7)
= 140.4 sq inches
Increase £140 by 5%.
Thank you so much
Answer:
£140 increased by 5% is £147.00
Answer:
it should be 147.00 , I'm so sorry if I'm wrong!
Fifteen students from Poppy High School were accepted at Branch University. Of those students, six were offered academic scholarships and nine were not. Mrs. Bergen believes Branch University may be accepting students with lower ACT scores if they have an academic scholarship. The newly accepted student ACT scores are shown here.
Academic scholarship: 25, 24, 23, 21, 22, 20
No academic scholarship: 23, 25, 30, 32, 29, 26, 27, 29, 27
Part A: Do these data provide convincing evidence of a difference in ACT scores between students with and without an academic scholarship? Carry out an appropriate test at the α = 0.02 significance level. (5 points)
Part B: Create and interpret a 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship. (5 points)
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A:
Given:
Pooled sample size: [tex]n=15[/tex]
Sample size (with academic scholarships): [tex]n_1=6[/tex]
Sample size (no academic scholarships): [tex]n_2=9[/tex]
Population standard deviations: Unknown
Sample mean (with academic scholarships): [tex]\bar{x}=\frac{25+24+23+21+22+20}{6}=22.5[/tex]
Sample mean (no academic scholarship):[tex]\bar{x}=\frac{23+25+30+32+29+26+27+29+27}{9}=27.\bar{5}[/tex]
Sample standard deviation (with academic scholarships): [tex]s_1=1.7078[/tex]
Sample standard deviation (no academic scholarships): [tex]s_2=2.5868[/tex]
Degrees of freedom: [tex]df=n-2=15-2=13[/tex]
Significance level: [tex]\alpha =0.02[/tex]
Decide which test is most appropriate to conduct:
Therefore, we will conduct a 2-sample t-test assuming our conditions are satisfied.
List null and alternate hypotheses:
[tex]H_o:\mu_1=\mu_2[/tex] -> There's no difference in ACT scores between students with and without an academic scholarship
[tex]H_a:\mu}_1\neq\mu_2[/tex] -> There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)
Determine the value of the test statistic:
We will use the formula [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }[/tex] to compute the test statistic [tex]t[/tex]. Therefore, the test statistic is [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }=\frac{27.\bar{5}-22.5}{\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9} } }=4.5592[/tex]
Calculate the p-value:
Because the test is two-sided, [tex]p=2tcdf(4.5592,1e99,13)=2(0.0003)=0.0006[/tex]
Interpret p-value and conclude test:
Given our significance level is [tex]\alpha =0.02[/tex], since [tex]p<\alpha[/tex], we reject the null hypothesis and conclude that there is significant evidence that suggests that there is a difference in ACT scores between students with and without an academic scholarship (it's more likely that the alternate hypothesis is true)
Part B:
The formula for a confidence interval for the difference in 2 population means is [tex]CI=(\bar{x}_1-\bar{x}_2)\pm t^*\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}[/tex] where [tex]\bar{x}_1-\bar{x}_2[/tex] is the difference of the 2 sample means and [tex]t^*[/tex] is the critical score for the desired confidence level.
The critical score for our 98% confidence interval would be [tex]t^*=invT(0.99,13)=2.6503[/tex]
Therefore, our 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is [tex]CI=(27.\bar{5}-22)\pm 2.6503\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9}}}=[2.6167,8.4944][/tex]
This means that we are 98% confident that the true difference in the ACT scores between students with and without an academic scholarship is contained within the interval [tex][2.6167,8.4944][/tex]
The evaluation of sub-parts results in:
Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02
Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]
How to perform two sample t-test?If the sample sizes < 30, and we want to test the difference between the sample means, then we perform t-test.
Let we have:
[tex]\overline{x}_1[/tex] = mean of first sample[tex]\overline{x}_2[/tex] = mean of second sample[tex]s_1[/tex] = standard deviation of first sample[tex]s_2[/tex] = standard deviation of second sample.Then, the value of t-test statistic is obtained as:
[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}[/tex]
If the level of significance is [tex]\alpha[/tex], then as we have:
the degree of freedom (d.f) = [tex]n_1 + n_2 - 2[/tex], the critical value of t is found to be [tex]t_{\alpha/2}[/tex], then if we get:
[tex]|t| < t_{\alpha/2}[/tex]null hypothesis
and if we get [tex]|t| > t_{\alpha/2}[/tex] null hypothesis, and thus, accept the alternate hypothesis.
For this case, we want to test if there is
Thus, we form the hypotheses as:
Null hypothesis: There's no difference in ACT scores between students with and without an academic scholarship
or: [tex]H_0: \mu_1 = \mu_2[/tex]
Alternative hypothesis: There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)
or [tex]H_1: \mu_1 \neq \mu_2[/tex]
where we have:
[tex]\mu_1[/tex] = population mean score of ACT of students having academic scholarship[tex]\mu_2[/tex] = population mean score of ACT of students having no academic scholarshipFor this case, we evaluate the mean and standard deviation as:
Sample 1: Academic scholarship: 25, 24, 23, 21, 22, 20Sample size = [tex]n_1 = 6[/tex]
Mean = sum of all observation/ number of observations = 135/6 =22.5
Thus, standard deviation = [tex]s_1 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_1})^2}} = \sqrt{\dfrac{17.5}{6}} \approx1.71[/tex]
Sample 2: No academic scholarship: 23, 25, 30, 32, 29, 26, 27, 29, 27Sample size = [tex]n_2 = 9[/tex]
Mean = sum of all observation/ number of observations = 248/9 ≈27.56
Thus, standard deviation = [tex]s_2 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_2})^2}} \approx \sqrt{\dfrac{60.22}{9}} \approx 2.59[/tex]
The t-test statistic is evaluated as:
[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}} = \dfrac{22.5 -27.56}{\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}}} \approx -4.56[/tex]
Degree of freedom = [tex]n_1 + n_2 - 2 = 6 + 9 - 2 = 13[/tex]
Level of significance = 0.02 = 2%
The critical value of t is found to be [tex]t_{0.02/2} =2.65[/tex]
Thus, we get: [tex]|t| \approx 4.56 > 2.65 =t_{\alpha/2}[/tex]
Thus, we may reject the null hypothesis.
That means, there is enough evidence of a difference in ACT scores between students with and without an academic scholarship at 0.02 level of significance.
Now, the 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is calculated as:
[tex]CI = (\overline{x}_1 - \overline{x}_2) \pm t_{\alpha/2}\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}\\\\CI = -5.06 \pm 2.65(\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}})\\\\CI \approx -5.06 \pm 2.65 \times 1.11\\CI \approx -5.06 \pm 2.94\\CI \approx [-5.06 - 2.94, -5.06 + 2.94] = [-7.00, -2.14][/tex]
Thus, the evaluation of sub-parts results in:
Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02
Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]
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A bag contains 8 apples and 6 oranges. You randomly draw a piece of fruit from the bag, eat it, and than randomly draw another. What is the probability you draw and eat an apple than draw an orange?
Answer:
[tex]probability \ of\ choosing\ apple\ first = \frac{8}{14}\\\\probability\ of\ choosing\ orange\ second = \frac{6}{13}\\\\probability \ of \ choosing \ apple \ and \then \ orange = \frac{8}{14} \times\frac{6}{13} = \frac{24}{91}[/tex]
To determine which window cleaner is most effective, Thad washes half of the windows in his house with one brand and the other half with a different brand. He then compares the results to draw a conclusion about which cleaner is most effective.
What kind of statistical study did Thad conduct?
A.
survey
B.
observational study
C.
theoretical study
D.
experiment
Answer:
the answer for the question is D,experiment
The kind of statistical study that Thad Conducted is called; Experiment
How to Identify Statistical Study?We ae told that we want to determine the cleaner that has the best effectiveness.
Now, since he compares the result of washing with let's say brand A to the result of washing with maybe brand B, then we can say that it is called an experiment due to the fact that it involves the procedure used to determine the efficacy or likelihood of something.
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Assume that you want to construct a box with a square base (closed top) and a volume of 1000 cm3 . Find the dimensions of the box to minimize the surface area of the box.
Answer:
[tex]x=10\sqrt[3]{2}[/tex]
Step-by-step explanation:
The Volume of a box with a square base
x by x cm and height h cm is
V =x^2h
The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.
The surface area of the box described is
A = x ^2 +4 x h
We need
A as a function of x alone, so we'll use the fact that
V= x^2h = 1000 cm^3
This imples [tex]h=\frac{1000}{x^2}[/tex]
This makes
[tex]A= x^2 + 4x(1000/x^2)\\A= x^2+4000/x[/tex]
Differentiating A w.r.t. x
[tex]A' = 2x-4000/x^2[/tex]
Now, A'=0
[tex]x=10\sqrt[3]{2}[/tex]
Therefore, minimum value x = [tex]x=10\sqrt[3]{2}[/tex]
Find the value of x that makes m∥n. PLEASEE HELP
Answer:
Step-by-step explanation:
143=5x+13(being corresponding angles)
143-13=5x
130/5=x
26=x
=======================================================
Explanation:
The angles shown are corresponding angles. Notice how they are in the northeast corner of their respective four-corner configuration.
If m is parallel to n, then the corresponding angles are congruent, and we can say...
5x+13 = 143
5x = 143-13 .... subtract 13 from both sides
5x = 130
x = 130/5 .... divide both sides by 5
x = 26
So taking this logic in reverse: if x = 26, then that leads to 5x+13 equal to 143, making the corresponding angles congruent. Therefore, it would lead to lines m and n being parallel.
3
Find the missing angle.
20
180°
A
100°
B
50°
80°
D 70°
What is
[tex] {5}^{7} [/tex]
Answer:
78,125
Step-by-step explanation:
5 × 5 × 5 × 5 × 5 × 5 × 5 = 78125
---------------------------------------------------------------------------------------------------------------
Have a good day :)
Write the fraction as a decimal and a percent. 13/9
Answer:
Decimal form = 1.44
Fraction form = 144/100
Hope this helps!
What is the value of 11g - 9k + 3 when g = 9 and k = 11?
Neatly show your work.
Answer:
3
Step-by-step explanation:
11g - 9k + 3
Let g = 9 and k =11
11 * 9 - 9*11 +3
Multiply
99 - 99 +3
Add
3
Answer:
3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
11g - 9k + 3
g = 9
k = 11
Step 2: Evaluate
Substitute in variables: 11(9) - 9(11) + 3Multiply: 99 - 99 + 3Subtract: 3p-8=3 can some one help me
Answer:
p=3+8=11
Step-by-step explanation:
Answer:
p = 11
Step-by-step explanation:
add 8 to both sides of the equation, so p = 3 + 8
p = 11
What percent of 8 is 6? pls give a detailed explanation thanks
Answer:
x/100 x 8 = 6
8x/100 = 6
x100 x100
8x = 600
Divide by 8 on both sides:
X = 75
Consider a percent out of 100. 'Of' meaning multiplication. 'is' meaning equal to that number.
(unknown number/percent)x/100 x 8(of 8) = 6(is 6)
Which of the following is the graph of (x + 3)2 + (y - 1)2 = 9? A B с 2. 2 2 2 4 -2 4 2 -2 2 2 4 2.
The third one is the correct graph for the equation
hope it helps !!
The equation [tex]\left(x-3\right)^{2}+\left(y-1\right)^{2}=3^{2}[/tex] is the equation of a circle. Graph B shows the given equation.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The standard equation of the circle is;
[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^{2}[/tex]
Where,
(h,k) are the coordinates of points on the x and y-axis.
r is the radius
The equation [tex]\left(x-3\right)^{2}+\left(y-1\right)^{2}=3^{2}[/tex] is the equation of a circle.
Hence, graph B shows the given equation.
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please help ASAP! 7th grade
Since their were no numbers to the questions i had to write it by the problem
Circle with 9 feet question
C=2(pi)r or C=(pi)d
Circular table question
A=(pi)r^2
Interest question
I=Prt
Volume of a rectangular prism
V=Bh
Triangular pyramid
V=1/3Bh
Returns on stock X are listed below: Period 1 2 3 4 5 6 7 Stock X 6% 5% -2% 10% 3% 8% -4% What is the mean of the data?
Answer:
The mean of the data is of 3.7143%.
Step-by-step explanation:
Mean of the data:
Sum of all returns divided by the number of returns.
Returns:
6% 5% -2% 10% 3% 8% -4%
7 returns.
Sum: 6 + 5 - 2 + 10 + 3 + 8 - 4 = 26%
Mean: 26%/7 = 3.7143%
The mean of the data is of 3.7143%.
35 POINTS!!!!
Every morning, Jorge runs a circular path that has a radius of 42 ft. How far does Jorge run if he does one lap around the track? Round your answer to the nearest foot. Use π=3.14.
A. 264 ft
B. 66 ft
C. 5,539 ft
D. 132 ft
what question is being asked ?
Answer:
4 meters
Step-by-step explanation:
Assuming that the garden is a rectangular garden, its area would be length ×width.
Let the length be L meters and the width be W meters.
Area= L ×W
48= LW -----(1)
Given that the length is 3 times the width,
L= 3W -----(2)
Substitute (2) into (1):
48= 3W(W)
3W²= 48
Divide both sides by 3:
W²= 48 ÷3
W²= 16
Square root both sides:
[tex]W = \sqrt{16} [/tex]
W= 4 (reject negative as width cannot be a negative number)
Thus, the width of the garden is 4 meters.
Hey help me out please?
Answer:
I believe it is C
It's the only one that makes sense
An equation with no solutions
3x + 7 = X + 3
Answer:
X = -2
Step-by-step explanation:
Hope this helps
please help! answer and step by step explanation needed
Answer:
Step-by-step explanation:
Due to the equation [tex]y = mx+c[/tex],
y = y
mx = [tex]\frac{2}{5}x[/tex]
c = -7
Hence, from 'mx',
m = 2/5
Hence, the slope is 2/5
Feel free to mark it as brainliest :D
Answer:
slope is
[tex] \frac{2}{5} [/tex]
Step-by-step explanation:
from the linear equation we consider the Cof of x is slope Y = a x ± b a is slope and b is intercept - y then 2/5 is slope and -7 is interceptASAP
-WILL MARK BRIANIST
Answer:
25 + x = y
Step-by-step explanation:
Answer:
25+x=y
Step-by-step explanation:
25 plus the birthday cards(x)= total cards(y)
pls help i need help
Answer:
Put x's on the numbers on the line that are above the line
Step-by-step explanation:
I BELIVE IN YOU
a chord 30cm long is 20cm from the centre of a circle. Calculate the length of a chord which is 24cm from the centre. please show workings
The length of a chord which is 24cm from the Centre is: 14 cm
How to find the length of the chord?Applying the Pythagorean theorem to the two right angle triangles that will be formed gives the radius of the circle from the first condition as:
R = √[(30/2)² + 20²]
R = √(15² + 20²)
R = √625
R = 25 cm
The length L of the another chord is calculated as:
L/2 = √(R² - 24²)
L/2 = √(25² - 24²)
L/2 = √49
L/2 = 7
L = 14 cm
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PLSSS HELP ASAP I NEED HELP
Jean took out a 5- year car loan of Rs 600 000.
He paid back a total of Rs 840 000.
What simple interest rate did he pay for this load?
interest= 840000-600000= 240000
P= 600000
R=?
t= 5 yrs
I = prt
240000 = 600000 × r × 5
r= 240000/600000×5
r = 0.08
interest rate = 0.08× 100 = 8%
A 25.5 foot ladder rests against the side of a house at a point 24.1 feet above the ground. The foot of the ladder is x feet from the house. Find the value of x to one decimal place.
Answer:
8.3
Step-by-step explanation:
Use the pythagorean theorem: a2 + b2 = c2 a2 would be 24.1 and c2 would be 25.5. square them then subtract a2 from b2. then find the square root of your answer which is 8.3
Find the distance from point A(2,-1) to the line y=-x+4
9514 1404 393
Answer:
(3/2)√2 ≈ 2.1213 units
Step-by-step explanation:
The distance d from point (x, y) to line ax+by+c = 0 is given by ...
d = |ax +by +c|/√(a^2 +b^2)
We can write the equation of the line as ...
x + y -4 = 0
so the distance is ...
d = |x + y - 4|/√(1^2 +1^2)
For point (x, y) = (2, -1), the distance is ...
d = |2 +(-1) -4|/√2 = 3/√2 = (3√2)/2
The distance from A(2, -1) to the line y = -x +4 is (3√2)/2 units.
Which expression is equivalent to (2x+3)(3x2−2x+5)?
Answer:
See the steps below:)
Step-by-step explanation:
Expression is equivalent to (2x+3)(3x²−2x+5) is 6x³+5x²+4x+15.
What are equivalent expressions ?An expression can be of many types numerical expressions, Algebraic expressions.We can also form these mathematical expressions from a given statement or by observing a real world scenario.
Equivalent expressions are same expressions in different forms.To check whether an expression is equivalent to another expression or not we just need to do some algebraic manipulations.Like distributing or taking common and other algebraic and arithmetic operations.
According to the given problem we have to write an expression which is equivalent to the expression (2x+3)(3x²-2x+5).
(2x+3)(3x²-2x+5)
= (2x+3)(3x²-2x+5)
=2x(3x²-2x+5)+3(3x²-2x+5) (now we will distribute)
=6x³-4x²+10x+9x²-6x+15
=6x³+5x²+4x+15.
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What is the area of a square if the base is 4.25ft and the height is 4.25 ft?
Answer:
18.0625 ft²
Step-by-step explanation:
4.25 × 4.25
18.0625 ft²