Answer:
C
Step-by-step explanation:
A cyclist travels 4 miles in 20 minutes and then a further 6 miles in 30 minutes without stopping. Calculate the cyclist's average speed in mph.
Answer:
24mph
Step-by-step explanation:
convert 20 mins and 30 mins to hrs by dividing by 60
4/(20/60)=12
6/(30/60)=12
12+12=24
Cyclist's average speed is 12 mph.
What is Speed?Speed is calculated as the ratio of the distance travelled by an object to the time taken to cover the distance.
It can also be defined as the rate of change of position of anything in any direction.
Speed is a scalar quantity as it does not have direction.
Total distance travelled by the cyclist = 4 miles + 6 miles
= 10 miles
Total time taken by the cyclist = 20 minutes + 30 minutes
= 50 minutes
We need the average speed in mph or miles per hour.
We know that,
60 minutes = 1 hour
1 minute = 1/60 hour
50 minutes = [tex]\frac{1}{60}[/tex] × 50 hour
= [tex]\frac{5}{6}[/tex] hour
Average Speed = Total distance travelled / Total time taken
= 10 miles / (5/6) hour
= 10 × [tex]\frac{6}{5}[/tex]
= 12 miles per hour
Hence the average speed of the cyclist is 12 miles per hour.
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A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer balancing the federal budget over cutting taxes; 59% of those asked said "yes." Suppose that in fact 62% of all adults favor balancing the budget over cutting taxes. If this poll was not biased, what is the probability you would get p^=0.59 or less?
Using the normal distribution and the central limit theorem, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sampling proportions of a proportion p in a sample of size n has mean [tex]\mu = p[/tex] and standard error [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]In this problem:
1,190 adults were asked, hence [tex]n = 1190[/tex]In fact 62% of all adults favor balancing the budget over cutting taxes, hence [tex]p = 0.62[/tex].The mean and the standard error are given by:
[tex]\mu = p = 0.62[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.62(0.38)}{1190}} = 0.0141[/tex]
The probability of a sample proportion of 0.59 or less is the p-value of Z when X = 0.59, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.59 - 0.62}{0.0141}[/tex]
[tex]Z = -2.13[/tex]
[tex]Z = -2.13[/tex] has a p-value of 0.0166.
0.0166 = 1.66% probability of a sample proportion of 0.59 or less.
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Which of the following equations names the same line as -2x – 3y = 5?
A. -4x - 6y = 12
B. -4x - y = 10
C. -6x - 9y = 15
D. 4x - 6y = 15
Answer:
c
Step-by-step explanation:
_6x -9y =15
_6x÷3=-2x
9y÷3=3y
15÷3=5
so,_2x -3y =5
Half of the marbles in a box are red, a third are white, and the other 6 are blue. Find the probability of picking a marble that is not blue
The probability of picking a marble that is not blue is 5/6
The proportions of the balls are given as:
[tex]Red = \frac 12[/tex]
[tex]White = \frac 13[/tex]
[tex]Blue = 6[/tex]
The probability of picking a ball that is not blue is:
[tex]P(Not\ Blue) = P(Red) + P(White)[/tex]
So, we have:
[tex]P(Not\ Blue) = \frac 12 + \frac 13[/tex]
Rewrite the fractions as equivalent fractions
[tex]P(Not\ Blue) = \frac 36 + \frac 26[/tex]
Take LCM
[tex]P(Not\ Blue) = \frac {3 + 2}6\\[/tex]
Add 3 and 2
[tex]P(Not\ Blue) = \frac {5}6[/tex]
Hence, the probability of picking a marble that is not blue is 5/6
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Please show your work !! 3and 4
Step-by-step explanation:
#3. 3^⅓ × 9^⅓ ......make the bases the same
3^⅓ × (3²) ^⅓
3^⅓ × 3^⅔ .....since the bases are the same, add the powers
3^ (⅓+⅔)
3^1
3
#4. ( x +6) ^ 3/5 = 8¹....multiply both sides by the reciprocal of 3/5
(x + 6) ^3/5 *5/3= 8^¹*5/4
x + 6 = 8^5/3
x + 6= ( 3√8)^5
x + 6 = 2^5
x + 6 = 32
x = 32 -6
x = 26
hope this helps!
Not sure though
Which is greater?
48 fl oz
10 3/4 c
The first step for deriving the quadratic formula from the quadratic equation, 0 = ax^2 + bx + c, is shown.
Step 1: –c = ax^2 + bx
Which best explains or justifies Step 1?
subtraction property of equality
completing the square
factoring out the constant
zero property of multiplication
Answer:
Subtraction property of equality
Step-by-step explanation:
You subtracted c from both sides of the equation to preserve equality
The step 1 is explained by subtraction property of equality.
The correct option is A.
The standard form of Quadratic Equation is
ax² + bx + c = 0
Also, we must remove c from the right side and move it to the left side in order to derive the quadratic formula from the quadratic equation.
And to do that, we must subtract c from both sides, which is
-c = ax² + bx
Then, we have used subtraction property here.
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Kiara bought fabric to make a dress and a sewing machine. The total cost of her purchase, $80.50, included both the cost of her sewing machine
Write an equation to determine the cost of fabric per foot
find the cost of fabric per foot
Order these numbers from least to greatest
Answer:
5.125, 5.14, ¹⁰³/₂₀, 5²/₉
Step-by-step explanation:
When you convert 103/20 to decimal you get 5.15 which is greater than 5.125 and 5.14.
When you convert 5²/₉ to fraction you get ⁴⁷/₉ which when converted to decimal is 5.222 which is greater than 5.125, 5.14 and 5.15.
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answer:
C
Step-by-step explanation:
y = 10
x = 8
The y intercept is 0 and the line runs through (0,0)
m = y / x This formula can only be used when the y incept is 0.
m = 10/8
m = 5/4
Equation
y = 5/4 x
3
pleaseee help lol also show work if you can please
Answer:
Answer is x = 31.5
Step-by-step explanation:
Explanation is in the picture. Pls give brainliest. :D
I forgot how to do this lol
Which statements are true about Gretchen's adjusted data set?
The data set is approximately symmetric.
The center moved farther from the center of Manuel's data set.
a The center moved closer to the center of Manuel's data set.
The spread values are closer to the spread values of Manuel's data set.
The data set is skewed left.
The spread values are farther from the spread values of Manuel's data set.
Answer:
The spread values are closer to the spread values of Manuel’s data set.
The data set is approximately symmetric.
The data set is skewed left.
Step-by-step explanation:
i got it right.
The true statements bout Gretchen's adjusted data set are (1), (4), and (5).
What are statistics?Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.
It is given that:
Which statements are true about Gretchen's adjusted data set:
The options are:
The data set is approximately symmetric.The center moved farther from the center of Manuel's data set.The center moved closer to the center of Manuel's data set.The spread values are closer to the spread values of Manuel's data set.The data set is skewed left.The spread values are farther from the spread values of Manuel's data set.As we know,
The spread values are more similar to Manuel's data set's spread values, and the data set is roughly symmetric and tilted to the left.
The true statements are:
The data set is approximately symmetric.The spread values are closer to the spread values of Manuel's data set.The data set is skewed left.Thus, the true statements bout Gretchen's adjusted data set are (1), (4), and (5).
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solve for x: 2-3(2x-2)=17
Answer:
x = - 1.5
Step-by-step explanation:
2 - 3(2x - 2) = 17 ← distribute parenthesis
2 - 6x + 6 = 17 , simplify
8 - 6x = 17 ( subtract 8 from both sides )
- 6x = 9 ( divide both sides by - 6 )
x = [tex]\frac{9}{-6}[/tex] = - [tex]\frac{3}{2}[/tex] = - 1.5
What is the equation of the line that passes through the point (5, 6) and has a slope
of 2
Answer:
y = 2x - 4
Step-by-step explanation:
Given:
x1 = 5
y1 = 6
slope (m) = 2
Solution:
y - y1 = m ( x - x1 )
y - 6 = 2 ( x - 5 )
y - 6 = 2x - 10
y = 2x - 10 + 6
y = 2x - 4
Triangle ABC is translated 2 units right and 5 units down to form triangle A’B’C’. This triangle is then translated 5 units right and 4 units up to form triangle A”B”C”. If the vertex A is at (-4, 2), what are the coordinates of vertex A”?
Answer:
(3,1)
Step-by-step explanation:
(x,y) (-4,2)
so -4 +2 = - 2 ; -2 +5 = 3
and for y: 2 - 5 = - 3 ; - 3 + 4 = 1
(3,1)
Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
Step-by-step explanation:
the scenario creates 2 similar triangles :
one main triangle with the house height the double floor distance and the double line of sight from the left point on the floor to the top of the house.
and the other triangle is the height of the tree, the single floor (from the left point to the tree) distance, and the single line of sight from the left point on the floor to the top of the tree.
similar triangles means : all angles are the same. and the side lengths of one triangle correlate to the corresponding side lengths in the other triangle by the same multiplication factor.
and that means that the floor distances of small and large triangle have the same ratio, as the view of line distance AND the height sizes.
we see : large triangle side / small triangle side = 2/1 = 2
and therefore, the same factor (2) applies to the heights.
so,
height of house / height of tree = 2
therefore,
height of tree = height of house / 2 = 150/2 = 75 ft
The perimeter of the figure below is 41.6 in.
Find the length of the missing side.
Answer:
the answer is 5.9 since both sides are the same and on the other side its 5.9
Hope This Helps!!!
3. In a survey of 200 people about a bus company, 77 said they were satisfied with the bus
company's performance. What percent of the people were satisfied with the bus company's
performance?
O 23%
38.5%
061.5%
077%
The percentage of the people that were satisfied with the bus company's performance is: B. 38.5%
Given the following data:
Population = 200 peopleSatisfied people = 77 peopleTo determine the percentage of the people that were satisfied with the bus company's performance:
In this exercise, you're required to find the number of the people that were satisfied with the bus company's performance as a percentage of the total population in this survey.
Thus, we would use this formula:
[tex]Percentage = \frac{Satisfied\;people}{Population} \times 100[/tex]
Substituting the given parameters into the formula, we have;
[tex]Percentage = \frac{77}{200} \times 100\\\\Percentage = \frac{77}{2}[/tex]
Percentage = 38.5%
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The formula for electrical energy, P, is P = I2R, where I is current and R is resistance. The formula for I in terms of P and R is ....
Answer:
[tex]i = \sqrt{ \frac{p}{r} } [/tex]
Your bank account starts with $1550 and every month $50 is automatically deducted for the cable bill. You want to know how long, x, it would take your account to drop below $0. How many months would it take for your account to drop BELOW $0?
Step-by-step explanation:
C(x) = 1550 - 50x
With C(x) the cash you have every month (x).
Now we solve:
1550 - 50x < 0
So it becomes:
50x > 1550
x > 31
The 32nd month you'll be broke.
STUDY
1. Simplify the expression below
5p + 14p
4(x - 2) + 6x
2. Evaluate
Answer:
(11)(B) Simplify numeric and algebraic expressions using the laws of exponents, including integral ... Evaluate the expression for d = -2, d = 0, and d = 1.
Step-by-step explanation:
Answer:
5p + 14p= 19p
4 (x-2)+6x
4x-8+6x
10x-8
Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
Answer:
75FT B
Step-by-step explanation:
if the building is 150 feet, then the tree is about 50% the height of the building it is 75 feet tall or answer B
Which number is closest to 1/2
Answer:
0.56
it's basically the number closest to 50. Don't get tricked by the 0.05 because that's only 5% not 50%
what are some expressions that are equivalent to
–
2(5n).
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\large\text{Gu\textbf{id}\textsf{e}}\bf\downarrow[/tex]
[tex]\large\textbf{2 negatives = positive}\\\large\textbf{2 positives = positive}\\\large\textbf{1 negative \& 1 positive = negative}\\\large\textbf{1 positive \& 1 negative = negative}\\\\\large\text{Negatives are BELOW 0}\\\large\text{Positives are ABOVE 0}\\\\\large\textsf{Negatives are on the LEFT side of zero.}\\\large\textsf{Positives are on the RIGHT side of zero.}[/tex]
[tex]\huge\textsf{-2(5n) \boxed{\rightarrow} \bf -10n}\\\\\\\\\huge\boxed{\rightarrow\text{-2n + (-2n) + (-2n) + (-2n) + (-2n)}}\\\huge\boxed{\rightarrow \text{\bf -2n - 2n - 2n - 2n - 2n}}\\\huge\boxed{\rightarrow{\text{-4n - 2n - 2n - 2n}}}\\\huge\boxed{\rightarrow \text{-6n - 2n - 2n}}\\\huge\boxed{\rightarrow \text{\bf -8n - 2n}}\\\huge\boxed{\rightarrow \boxed{\text{ -10n}}}[/tex]
[tex]\huge\text{\bf -5(2n)}\\\huge\boxed{\rightarrow \text{-10n}}[/tex]
[tex]\huge\boxed{\text{\bf Therefore, your answers \underline{\underline{could}} be: }}\\\huge\boxed{\bullet \textsf{ -2n - 2n - 2n - 2n -2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -8n - 2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -5(2n)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the common ratio of the geometric sequence 9, -18, 36, ...
Answer:
-2.
Step-by-step explanation:
-18/9 = -2.
36/-18 = -2.
We multiply by -2 to get the next number in the sequence.
Common ratio is -2.
Which property is shown here? (-3 + 9) + 1 = -3 + (9 + 1)
Answer:
Commutative property
Step-by-step explanation:
Answer:
Associative property I think
Step-by-step explanation:
how many roots does the quadratic function h(x)+=x2^2-3x+6 have
The quadratic function h(x) = x² - 3x + 6 has 2 roots.
A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.
Polynomials are classified based on degree as linear, quadratic, cubic etc.
A quadratic polynomial has a degree of 2, hence it has only 2 roots.
The quadratic function h(x) = x² - 3x + 6 has 2 roots.
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if a is more than b, what is the equation for an ellipse with a centre at the origin and a horizontal major axis?
Answer:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
97 term of-5,-23,-41
Answer:
-1147
Step-by-step explanation:
Answer:
-1733
Step-by-step explanation:
-5-96*18 = -1733