\(\cos(H )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{\sqrt{73}}} \implies \cos(H)=\cfrac{3}{\sqrt{73}}\cdot \cfrac{\sqrt{73}}{\sqrt{73}} \implies \cos(H)=\cfrac{3\sqrt{73}}{73}\)
Développer et réduire (3 − 2)² + (7 + 5)(3 − 2)
\((3-2)^2+(7+5)(3-2)=(3-2)(3-2)+(7+5)(3-2)=(3-2)(3-2+7+5)=1*13=13\)
find reason and statements
Answer:
Missing reason/statements:
R1, R2, R3 - GivenS4. ∠1 ≅ ∠3R4. Transitive propertyR5. Definition of congruenceS6. m∠1 = 120°R6. SubstitutionOne brand of cola co fizz is sold in packs of 4*500ml for 2.50 another brand colo is sold in packs of 10 330mlfo $2 which brand is more expensive
Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.
To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.
For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.
For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.
Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.
Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.
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Monty invested $8600 in a savings account with a yearly interest rate of 5% for 12 years. How much sinple interest did he earn.
Answer:
$5160
Step-by-step explanation:
Each year, he earns 5% of 8600 = 0.05 * 8600 = $430
After 12 years, she will earn 12 * 430 = $5160 in interest
What is the shape of the cross section of the figure that is perpendicular to the triangular bases and passes through a
vertex of the triangular bases?
A
a parallelogram that is not a rectangle
O a rectangle
O a triangle that must have the same dimensions as the bases
O a triangle that may not have the same dimensions as the bases
Answer:
a triangle that may not have the same dimensions as the bases
Step-by-step explanation:
The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.
A medical school claims that more than 28% of its students plan to go into general practice. To test this claim, a random sample of 130 of the school's students is selected. Of these, 32% of them plan to go into general practice. Find the P-value for this test of the school's claim.
Answer:
The p-value of the test is 0.1314.
Step-by-step explanation:
In this case we need to test the claim made by a medical school that more than 28% of its students plan to go into general practice.
The hypothesis can be defined as follows:
H₀: The proportion of students planning to go to general practice is 28%, i.e. p = 0.28.
Hₐ: The proportion of students planning to go to general practice is more than 28%, i.e. p > 0.28.
The information provided is:
n = 130
\(\hat p=0.32\)
Compute the test statistic value as follows:
\(z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}\)
\(=\frac{0.32-0.28}{\sqrt{\frac{0.28(1-0.28)}{130}}}\\\\=1.12\)
The test statistic value is 1.12.
Compute the p-value as follows:
\(p-value=P(Z>1.12)\\\)
\(=1-P(Z<1.12)\\\\=1-0.86864\\\\=0.13136\\\\\approx 0.1314\)
The p-value of the test is 0.1314.
*Use the z-table.
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
The complete question is attached in the diagram.
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Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 145 millimeters, and a standard deviation of 7 millimeters. If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would be less than 141.5 millimeters? Round your answer to four decimal places.
Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).
What is probability?Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It is expressed as a value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur.
According to question:To solve this problem, we can use the formula for the standard deviation of the sample mean:
Standard deviation of sample mean = standard deviation / √(sample size)
Plugging in the given values:
Standard deviation of sample mean = 7 / √(31)
Next, we can calculate the z-score, which is the number of standard deviations the sample mean is below the population mean:
z-score = (sample mean - population mean) / standard deviation of sample mean
Plugging in the given values:
z-score = (141.5 - 145) / (7 / √(31))
Using a calculator, we find that the z-score is approximately -2.22.
Finally, we can use a standard normal distribution table or a calculator to find the probability that a z-score is less than -2.22.
Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).
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Out of numbers: 5, 7, 21, 25, 28, 35, 42, 56, 75, and 80, choose those which are multiples of 4 or 7
Answer:
Multiples of 4= 28
Multiples of 7= 7,21,28,35,42
Step-by-step explanation:
I hope this helps, and have a great day! :)
The solution set of Vx - 2 = -2 is:
B. (-6)
C. 1-2)
none of these
What is the length of arc S shown below?
S
2
7 cm
The angle in the figure is a central angle in radians.
Answer: S= 14 cm
Step-by-step explanation:
Answer: 14
Step-by-step explanation: Khan Academy
In the figure below, mZ2-66". Find m21, mZ3, and mZ4
*
m23-
#24-
%
The value of the angles in the figure are:
m∠1 = 114°
m∠3 = 114°
m∠4 = 66°
How to find m∠1, m∠3 and m∠4 in the figure?To answer the question, we need some angle geometry knowledge:
We have:
m∠2 = 66°
Thus, we can find the angles in the figure as follow:
m∠1 = 180° - 66° (sum of angles on a straight line is 180°)
m∠1 = 114°
m∠3 = m∠1 (vertically opposite angles are equal)
m∠3 = 114°
m∠4 = m∠2 (vertically opposite angles are equal)
m∠4 = 66°
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given line t below, choose all points that lie on the line that passes through point P and is parallel to line t.
Answer:
the answer is 4 and 3
Step-by-step explanation:
taking the point on x and y axis so u get 4 and 3
Find x
proportions with similar triangles.
Answer:
32
(this is just an approximation due to the left triangle)
You have $50 and a $15 gift card to spend online. You purchase a pair of headphones for $34.99 and 8 songs for x dollars each. Use an algebraic expression to find the amount you have left when each song costs $1.10.
Answer:
50 + 15 -34.99 - 8x
65 - 34.99 - 8(1.10)
30.01 - 8.8
$21.21
Step-by-step explanation:
The amount you have left when each song costs $1.10 is $21.21.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
You have $50 and a $15 gift card to spend online.
Cost of each sing = $1.10
You purchase a pair of headphones for $34.99 and 8 songs for x dollars each,
Calculate the total amount as shown below,
Total cost = cost of headphones + cost of each song × number of songs
Total cost = 34.99 + 1.10 × 8
Total cost = 34.99 + 8.8
Total cost = $43.79
Calculate the remaining cost as shown below,
Remaining cost = $50 + $15 - total cost
Remaining cost = $65 - $43.79
Remaining cost = $21.21
Therefore, the amount you have left when each song costs $1.10 is $21.21.
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Write 3 more equations using the same numbers that express the same relationship.
Equation: 3 + 2 = 5
Answer:
2+3 = 5
5-2 = 3
5-3 = 2
Step-by-step explanation:
Amanufacturer of potato chips would like to know whether its bag filling machine works correctly at the 433 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 427 grams with a variance of 324. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answer:
There is not enough evidence to support the claim that the bags are under filled.
Step-by-step explanation:
Given :
Population mean, μ = 433
Sample size, n = 26
xbar = 427
Variance, s² = 324 ; Standard deviation, s = √324 = 18
The hypothesis :
H0 : μ = 433
H0 : μ < 433
The test statistic :
(xbar - μ) ÷ (s/√(n))
(427 - 433) / (18 / √26)
-6 / 3.5300904
T = -1.70
The Pvalue :
df = 26-1 = 25 ; α = 0.05
Pvalue = 0.0508
Since Pvalue > α ; WE fail to reject the Null and conclude that there is not enough evidence to support the claim that the bags are underfilled
Pls help
Which of these rational number's is the product of the other 6:
2/99, 2/3, 5/7, 2 1/3, 2 1/4, 10/11, 18.
Answer:
10/11
Step-by-step explanation:
Find the midpoint of a line segment with endpoints at left parenthesis negative 5 comma negative 4 right parenthesis and left parenthesis 7 comma space 6 right parenthesis.
\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 7 -5}{2}~~~ ,~~~ \cfrac{ 6 -4}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies (1~~,~~1)\)
Estimate the sum of 379+409=
Answer:
Round both numbers to 1 significant figure.
400+400=800
800 is the answer.
HELP ME!!!!
ZEARN!!!!!!!!!
A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.
Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.
Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.
Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of
To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).
First, let's convert the fractions 1/5 and 2/3 to fifteenths:
\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)
\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)
Now we can rewrite the expression using the common denominator:
\(3 + \frac{3}{15}+\frac{10}{15}\)
Steve says to find the difference in temperature between 7 AM and
12 PM Wednesday, he can use a number line. He says because one
temperature is negative and the other is positive, he can add together their
distances from 0.
Kelly says that she can find the change by subtracting -5.1 from the temperature
at 12 PM on Wednesday.
Who is correct? Use the drop-down menus to explain your reasoning and find the
change in temperature.
and the distance from 0 to the Wednesday 12 PM temperature is 2.5
Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.
By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.
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simplify [Xn (X'nY)]'.
Answer:
(X'U'Y) + (XUY')
Step-by-step explanation:
Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:
[Xn(X'nY)]' = (Xn)' + (X'nY)'
Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:
(Xn)' + (X'nY)' = (X'U'Y) + (XUY')
where U represents the logical operator "or".
Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').
Which pile of laundry has more shirts?
Pile 1
Three pants two shirts
Pile 2
Two shirts 4 pants
Answer:111
Step-by-step explanation:
1111
Angelina puts 3,000 milliliters of water in a tub that already has 5 liters of water in it. Jack says the tub now has 35 liters of water in it. Angelina explain he is wrong. Explain who is correct and why
Answer:
-Angelina is correct
Explaintion: Jack in incorrect because it seems that he messed up is place order. He might have thought that 1 liter is equal to 100 mililiters instead of 1,000. That way he might have gotten 30+5=35 instead of 5+3=8
Step-by-step explanation:
3000 ML+ 5L
1 milliliter has 0.001 liters in it.
3000ML= 3L
Angelina has 8 lieters of water in the tub now.
A coach of a baseball team orders hats for
the players on his team. Each hat costs
$9.95. The shipping charge for the entire
order is $5.00. There is no tax on the order.
The total cost of the coach's order is less
than $125.00. Which inequality can be
used to determine the greatest number of
hats, h, the coach orders?
Answer:
9.95h + 5 ≤ 125
Step-by-step explanation:
let 'h' = number of hats
If 600 bolts were already examined and 12 were defective, determine the probability that next bolt found would be nondefective.
The probability that the next bolt found would be non-defective is 0.98 or 98%.
What is Probability Theory?A fundamental idea in mathematics and statistics, probability theory has several uses in the sciences, engineering, business, and social sciences. It is used to assess risks and uncertainties in diverse circumstances, analyse and forecast the possibility of events happening, and make decisions in the face of uncertainty.
Given:
Number of bolts already examined = 600
Number of defective bolts found = 12
Number of non-defective bolts = Total number of bolts examined - Number of defective bolts
= 600 - 12
= 588
Probability of finding a non-defective bolt = Number of non-defective bolts / Total number of bolts
= 588 / 600
= 0.98 or 98%
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which represents the rotation of ABC toA’B’C
a:(x,y) —> (-x,-y)
b:(x,y) —> (x,-y)
c:(x,y) —> (y, -x)
Answer:
a) A (-2,-2) →A¹ ( 2, 2)
B (-5,-2) →B¹ (5 , 2)
C (-3,-4) →C¹ ( 3 ,4))
b)
A (-2,-2) → A¹( -2, 2)
B (-5,-2) →B¹ (-5 , 2)
C (-3,-4) →C¹ ( -3 ,4))
c)
A (-2,-2) → A¹( -2, 2)
B (-5,-2) →B¹ (-2 , 5)
C (-3,-4) →C¹ ( -4 ,3))
Step-by-step explanation:
a) Given the (-2,-2) is rotation 180° of counter clock wise then the transformed
to A (-2,-2) → A¹( 2, 2)
B (-5,-2) →B¹ (5 , 2)
C (-3,-4) →C¹ ( 3 ,4))
b)
Reflection about the x-axis
( x, y) → ( x, -y)
A (-2,-2) → A¹( -2, 2)
B (-5,-2) →B¹ (-5 , 2)
C (-3,-4) →C¹ ( -3 ,4))
c)
( x, y) → ( y, -x)
Given (x, y) is rotation 90° of clock wise about the origin then the transformed to
A (-2,-2) → A¹( -2, 2)
B (-5,-2) →B¹ (-2 , 5)
C (-3,-4) →C¹ ( -4 ,3))
The 7th grade basketball team has won 15 games out of the 20 games they have played this season. If they were to keep up this winning ratio, what is the probability they will win their next game?
Answer: 3/4
Step-by-step explanation:
What is the volume of a cylinder, in cubic cm, with a height of 19cm and a base
diameter of 10cm? Round to the nearest tenths place.
Answer:
549.8 cm (cubed)
Step-by-step explanation:
D3lt4 m4th 4n$wer