The statements about the number -27 that are true are given as follows:
-27 is an integer number.-27 is a rational number.What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.
Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.
Integer numbers are numbers that have no decimal part, hence -27 is an example of an integer number, which are also rational numbers.
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Chapter 3: Probability (Add and Mult)
Score: 22.75/38 26/38 answered
Question 29
>
A bag contains 7 red marbles, 5 white marbles, and 6 blue marbles. You draw 3 marbles out at random,
without replacement. Find the following probabilities and round to 4 decimal places.
a. The probability that all the marbles are red is
b. The probability that none of the marbles are red is
a. The probability that all the marbles are red is calculated as follows:
(7 choose 3) / (18 choose 3) = (35 / (816)) = 0.0429
So, the probability that all the marbles are red is 0.0429, rounded to 4 decimal places.
b. The probability that none of the marbles are red is calculated as follows:
(12 choose 3) / (18 choose 3) = (220 / 816) = 0.2696
So, the probability that none of the marbles are red is 0.2696, rounded to 4 decimal places.
A baseball coach purchased bats and batting helmets. The coach purchased 19 items in all. Each bat cost $18.25 and each batting helmet cost $24.50. If the coach spent a total of $396.75, how many bats did the coach purchase?
Answer:
11 bat and 8 helmets.
Step-by-step explanation:
Let x = the number of bats
Let y = the number of batting helmets
x + y = 19 Rewrite as y = 19 - x
18.25x + 24.50y = 369.75 Multiply by 100
1825x + 2450y = 36975 Substitute 19 - x for y
1825x + 2450(19 -x) = 39675 Distribute the 2450
1825x + 46550 - 2450x = 39675 combine like terms
-625x + 46550 = 39675 subtract 46550 from both sides
-625x = -6875 Divide both sides by -625
x = 11
He bought 11 bats
x + y = 19 Substitute 11 for x to solve for y
11 + y = 19 Subtract 11 from both sides
y = 8
He bought 8 helmets.
Find the circumference of a circle with a diameter of 8 inches
Answer:
B
Step-by-step explanation:
c=d*π
c=8*π
c=25.1 inches
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In a running race, you covered 3000 m. The ratio of distance covered by walking to running is 2:13. How many meters did you walk?
Answer:
400 m walking
Step-by-step explanation:
sum the parts of the ratio , 2 + 13 = 15 parts
divide the distance covered by 15 to find the value of one part of the ratio.
3000 m ÷ 15 = 200 m
then
2 parts = 2 × 200m 400 m
400 m covered by walking
The Robinson family ordered snacks at the State Fair. They bought the
following drinks (d), pizza (p), and ice cream cones (c).
Answer:
a. 2p + 2d + 1c + 1p + 1c + 2p + 1d
b. 5p + 3d + 2c
c. In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.
This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)
Step-by-step explanation:
a.
From the cute diagram we see that the family bought
2 pizzas + 2 drinks + 1 cone + 1 pizza + 1 cone + 2 pizzas + 1 drink
Using the variables provided, this becomes
2p + 2d + 1c + 1p + 1c + 2p + 1d
b.
Combining like terms the total purchase is:
(2p + 1p + 2p) + (2d + 1d) + (1c + 1c)
Adding the coefficients of each grouped term we get
(5p) + (3d) + (2c)
Opening the brackets, this becomes
5p + 3d + 2c
c.
In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.
This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)
Which of the following is something you would not expect to see on a basic loan application?
On solving the provided question, we can say that expression is - doctor’s name and address, EDG 2020
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
expression is -
doctor’s name and address
EDG 2020
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The correct question is -
Which of the following is something you would not expect to see on a basic loan application?
a. employer's name and address
b. doctor's name and address
C. annual or monthly income
d. current monthly rent or mortgage payment
Please select the best answer from the choices provided
A boat has a top speed of 26 knots and a displacement of approximately 81000 tons. (1 knot= 1 nautical mile per hour; 1 metric tonne =1000 kilograms)
On solving the provided question we can say that 2 decimal places =29.92 miles per hour
what is decimal?Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the
top speed is 26 knots,
1 knot = 1.15078 miles per hour
26 knots = 26 * 1.15078
= 29.92028 miles per hour
2 decimal places
=29.92 miles per hour
boat has a displacement of 96000 tons
1 ton = 0.907185 metric tonnes
96000 tons = 0.907185 * 96000
= 87,089.76 metric tonnes
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The inequalities 3x<1 and 6x<2 are equivalent inequalities. Write another inequality that is equivalent to 3x<1 and 6x<2.
One inequality that is equivalent to 3x<1 and 6x<2 is 3x<1/2.
To see why this is true, we can divide both sides of the second inequality by 2, which gives 3x<1/3. However, we want an inequality that is equivalent to both 3x<1 and 6x<2, so we need to find a common solution.
Notice that if 3x<1, then x<1/3. And if 6x<2, then x<1/3 as well (since 1/3 is less than 2/6). Therefore, the intersection of the solutions for these two inequalities is x<1/3.
But we want an inequality in the form of 3x<a, where a is some constant. To find this value, we need to solve for x in the intersection of the two solutions:
x<1/3
Multiplying both sides by 3 gives:
3x<1
So we can choose a=1/2, which gives us the final inequality:
3x<1/2
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19. For the period 2009-2013, if T is the number (in millions) of
Comcast video subscribers, then 7 10.3 is approximately the
number (in millions) of Time Warner Cable video subscrib-
ers (Source: Comcast, Time Warner Cable). There were about
21.7 million Comcast video subscribers in 2013. Estimate the
number of Time Warner Cable video subscribers in 2013.
The estimated number of Time Warner Cable video subscribers in 2013 is approximately 14.8 million.
Estimation by ProportionsWe are given that for the period 2009-2013, 7/10.3 is approximately the number of Time Warner Cable video subscribers for every Comcast video subscriber. We are also given that there were 21.7 million Comcast video subscribers in 2013.
To estimate the number of Time Warner Cable video subscribers in 2013, we can use the following proportion:
7/10.3 = x/21.7
where x is the number of Time Warner Cable video subscribers in 2013.
Solving for x, we get:
x = (7/10.3) x 21.7
x ≈ 14.8 million
Therefore, the estimated number of Time Warner Cable video subscribers in 2013 is approximately 14.8 million.
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You randomly pull a marble from a bag of marbles. The bag has 2 red
marbles, 1 pink marble, 1 green marble, and 5 speckled marbles,
What is the probability of not drawing a green marble? Write your
answer as a decimal rounded to the nearest hundredth.
A
Answer:
0.89
Step-by-step explanation:
As there is 1 green marble out of 9 total marbles, there's a 1 in 9 chance of selecting the green marble. This means that its complement would be the probability of NOT selecting the green marble would be 8/9, or about 0.89
Answer:0.89
Step-by-step explanation:
For the transformation to be a translation, which statements are true? Select four options
Answer:
do it yourself
Step-by-step explanation:
Answer:
A. The transformation preserves distances and angles between points.
B. The transformation preserves the orientation of the figure.
C. The transformation involves a sliding of the figure in a fixed direction.
D. The transformation results in a change of size or shape of the figure.
E. The transformation results in a reflection of the figure.
For the transformation to be a translation, statements A, B, C and E are not true, while statement D is true.
Step-by-step explanation:
Find HP
Round to the nearest whole meter
Check the picture below.
Make sure your calculator is in Degree mode.
Box plot pls help outliers
The boxplot without the outliers is (c)
What are outliersOutliers are data points that are significantly different from the other data points in a dataset.
An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.
How to determine the boxplotUsing the definition in (a) as a guide, we have the boxplot to be (c)
This is so because it has a minimum of 15 and a maximum of 95 (just as the original boxplot)
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Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 51.8 degrees.
Low Temperature
(circle◦F)
40minus−44
45minus−49
50minus−54
55minus−59
60minus−64
Frequency
22
55
1212
77
11
The mean of the frequency distribution is____ degrees. (Round to the nearest tenth as needed.)
Which of the following best describes the relationship between the computed mean and the actual mean?
A. The computed mean is close to the actual mean because the difference between the means is less than 5%.
B. The computed mean is not close to the actual mean because the difference between the means is less than 5%.
C. The computed mean is not close to the actual mean because the difference between the means is more than 5%.
D. The computed mean is close to the actual mean because the difference between the means is more than 5%.
The mean of the frequency distribution is 52 degrees. and option A is carrect . A) The computed mean is close to the actual mean because the difference between the means is less than 5%
First, we calculate the class mid-points (x); This is the mean of the class intervals.
For 40 - 44, x = (40 + 44)/2 = 42. This is applied to all other classes.
40 −44 = 42
45 −49 = 47
50 −54 = 52
55 −59 =57
64 −64 = 62
So:
x 42 47 52 57 62
f 22 55 1212 77 11
mean = ∑f(x)/∑f
= (42*22+47*55+52*1212+57*77+62*11)/(22+55+1212+77+11)
= 71604/1377
=52
actual mean = 51.8
and now mean = 52
percentage difference = ((52-51.8)/51.8)*100
= 0.3861 percentage
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How to transform the graph of a function using more than one transformation
The transformation used are:
(a)
This is a translation of one unit to the left and one unit up.
(b)
- There is a vertical stretch of 2 units.
- This is a translation of four units down.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The graph from y = h(x) to y = h(-x) + 1.
This is a translation of one unit to the left and one unit up.
The graph from y = g(x) to y = 2g(x) - 4.
- There is a vertical stretch of 2 units.
- This is a translation of four units down.
Now,
The graph of y = h(-x) + 1 is given below.
The graph of y = 2g(x) - 4 is given below.
Thus,
(a)
This is a translation of one unit to the left and one unit up.
(b)
- There is a vertical stretch of 2 units.
- This is a translation of four units down.
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The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a standard deviation of 0.04. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.04, Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H, and the alternative hypothesis H, that we would use for this test. P KQ 0 Oso X X a Р S 00 020
The null hypothesis H0 in this case would be that the standard deviation of the number of accidents per day is equal to 0.04, while the alternative hypothesis Ha would be that the standard deviation of the number of accidents per day is not equal to 0.04.
The null hypothesis represents the status quo or the default assumption, which is that there has been no change in the standard deviation of the number of accidents per day. The alternative hypothesis represents the claim made by the actuaries, which is that there has been a change in the standard deviation.
Mathematically, the null and alternative hypotheses can be expressed as follows:
H0: σ = 0.04
Ha: σ ≠ 0.04
where σ represents the standard deviation of the number of accidents per day.
The hypothesis test would be used to determine whether there is evidence to support the actuaries' claim that the standard deviation has changed, or whether there is not enough evidence to reject the null hypothesis that the standard deviation remains equal to 0.04.
Rowan was collecting seashells she collects 4 more than three times the number of seashells Maribel collects if Maribel collects X seashells select the expression of represents the number of seashells Rowan collects
Answer:
Rowan collects
3x + 4
Step-by-step explanation:
Maribel collects x sea shells.
Rowan collects 4 more (this is the +4)
than 3 times Maribels (this is the 3x)
Maribel = x
Rowan = 3x + 4
Answer:
its actually 4x + 3
Step-by-step explanation:
3 1/5+n=9 which can be used to solve this equation
If a graph of y=-9x + 11 were changed to a graph of y=-9x+14, how would the y-intercept change? OA. The y-intercept of the new graph would shift up 3 units. B. More information is needed to determine the change. C. The y-intercept would remain the same. D. The y-intercept of the new graph would shift down 3 units.
Answer:
Step-by-step explanation:
The y-intercept of a linear equation in slope-intercept form, y = mx + b, represents the point at which the line crosses the y-axis. In this form, "m" represents the slope of the line and "b" represents the y-intercept.
If we have a graph of y = -9x + 11, the y-intercept can be found by setting x equal to 0 and solving for y:
y = -9x + 11
y = -9 * 0 + 11
y = 11
So, the y-intercept of the original graph is (0, 11).
Now, if we have a graph of y = -9x + 14, the y-intercept can be found in the same way:
y = -9x + 14
y = -9 * 0 + 14
y = 14
So, the y-intercept of the new graph is (0, 14).
Comparing the y-intercepts of the two graphs, we can see that the y-intercept of the new graph has shifted up by 3 units, from (0, 11) to (0, 14).
Therefore, the correct answer is A: The y-intercept of the new graph would shift up 3 units.
Find the inverse of each of the given functions.
f(x)=4x-12
DONE
+
h(x)
O
O
H
2x - 4
3
h¯¹(x) = 3x - 12
2
h¯¹(x) =
h"¹(x) =
DONE
3
(2x - 4)
3x + 4
2
Answer:B
Step-by-step explanation:
In an isosceles triangle, one angle is 24° greater than each of the other two equal angles.
Find the measure of all three angles.
The two smaller angles are each _____
The two smaller angles are 39 degrees each. The other angle is 106
How to solve for the anglesThe measure of the angles would be found using the formula
2*x + 24 = 180
This is because the sum of angles that are in a triangle is = 180
the two equal angles are x + x = 2x
the other angle is 24 greater than 2x
2x + 24 = 180
2x = 180 - 24
2x = 156
x = 78
eaxh of the two equal angles are 78 degrees
while the other angle is 78 + 24 = 106
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Consider a linear function where
F(-10)=64 and f(15)=54
Find the equation
The equation is f(x) = -0.4x + 60. The solution has been obtained by using slope - intercept form.
What is slope-intercept form?
The graph of the equation y = mx + b is a line with a slope of m and a y-intercept of b. The form of the linear equation is called the slope-intercept form, and the values of m and b are real integers.
We are given that f(-10) = 64 and f(15) = 54.
So, we get the points as (-10 , 64) and (15 , 54)
Using the slope intercept form, we get
Slope(m) = (54 - 64)/(15 + 10)
Slope(m) = -0.4
We know that y = mx + b
For calculating b. we will put in the values
⇒64 = -0.4(-10) + b
⇒64 = 4 + b
⇒b = 60
From this we get the equation as
f(x) = -0.4x + 60
Hence, the equation is f(x) = -0.4x + 60.
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The entry ticket to a local museum costs $12 for an adult and $8 for a child. A group of 100 people paid an entry fee of $1,056. How many adults and how many children were there in this group?.
The number of adults and children in the group were 64 and 36 respectively by using an algebraic equation.
It is given that the entry ticket to a local museum costs $12 for an adult and $8 for a child. A group of 100 people paid an entry fee of $1,056.
Let the number of adults in the group = x
number of adults in the group = y
Total number of people paid an entry fee = 100
So the equation becomes : x + y = 100
or x = 100 - y
Cost for adult ticket = $12
Cost for child ticket = $8
Total entry fee paid = $1,056
Second equation = 12x + 8y = 1056
putting value of x from equation 1
12(100 - y) + 8y = 1056
1200 - 12y + 8y = 1056
4y = 144
y = 36
x = 100 - 36 = 64
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Write the equation of the transformation of g(x) = 4* by shifting up 2, shifting right 5, reflecting over the
X -axis, and then horizontally compressing by a factor of 5.
f(x) =
The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
g(x) = 4ˣ
The function is shifting up 2 and shifting right 5. Then the function is given as,
g(x) = 4⁽ˣ⁺⁵⁾ + 2
The function after reflecting over the x-axis is given as,
- g(x) = 4⁽ˣ⁺⁵⁾ + 2
g(x) = - 4⁽ˣ⁺⁵⁾ - 2
And then horizontally compressing by a factor of 5. Then the function is given as,
f(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2
The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.
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To get a free meal at his favorite restaurant in town needs to spend $50 or more at the restaurant he has already spent $30.25. How much more does Tom need to spend to get his free meal?
Write an inequality to solve the problem
Answer:
x [tex]\geq[/tex] 19.75
Step-by-step explanation:
x ≥ 50 - 30.25
x ≥ 19.75
To get a free meal, he needs to spend 19.75 or more.
Geometry teacher doesnt teach
The area of the kite is 0.08 metres squared.
How to find the area of a kite?A kite is a quadrilateral. Therefore, the window has the shape of a kite. The square metres of glass that will be used to construct the kite can be calculated as follows:
The area of a kite is half the products of the diagonals of the kite.
Therefore,
area of the kite = 1 / 2 pq
where
p and q are the diagonals.Therefore,
p = 20 + 20 = 40 cm
q = 25 + 15 = 40 cm
Hence,
area of the kite = 1 / 2 × 40 × 40
area of the kite = 1600 /2
area of the kite = 800 cm²
area of the kite = 0.08 m²
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The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27
What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.
Answer:
the IQR is the best measure which equals 16
Step-by-step explanation:
the 2nd option is not correct because, while the range is 45, there are only two out of eleven data items above 45, which is not representative of the majority of the data
the 3rd option is incorrect because the IQR does not equal 45, it's 16
the 4th option is incorrect because the range does not equal 16, it's 45
What is the actual length which is represented by 3.2cm on a scale drawing with scale 1cm to 4cm
Answer: 12.8 cm
Step-by-step explanation:
Multiply 3.2 by the scale of 4 to get 12.8.
Given right triangle ABC with altitude
BD drawn to hypotenuse AC. If
AC 36 and DC = 9, what is the length
of BC?
=
C
9
D
36
X
A
B
Can someone please helppp
The measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangles; ∆ABC with hypotenuse = 45 and adjacent = BC, the triangle ∆ADC with hypotenuse = BC and adjacent = 9 with the angle C we can solve for BC as follows:
for ∆ABC;
cosC = 9/BC {adjacent/hypotenuse}
for ∆ADC;
cosC = BC/45 {adjacent/hypotenuse}
9/BC = BC/45
BC² = 9 × 45 {cross multiplication}
BC² = 405
BC = √405 {take square root of both sides}
BC = 20.1246
Therefore, the measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C
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Hercules crawled on fifth of a mile in a one tenth of an hour. find the rate in miles per hour
In linear equation, 2 miles per hour is the rate in miles per hour .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Divide the distance by the time.
(1/5 miles) / (1/10 hour)
= 10(1/5) miles per hour
= 2 miles per hour
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