The Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.
As per the question we need to create a division problem where both the divisor and the dividend are decimals and the quotient must be a whole number greater than 1.
So, Let us suppose divisor as 1.5 . Now the dividend must be a decimal number which is greater than 1.5, let's say 5.5.
Now on dividing 5.5 by 1.5,
Divisor = 1.5
Dividend = 4.5
(Dividend/Divisor) = ( 4.5 / 1.5 ) = 3
Quotient = 3
On dividing dividend by divisor the quotient is 3 which is a whole number greater than 1.
So, we can conclude that the Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.
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During training, an athlete ran 250m/min. But then on the day of the race, he increased his average speed to 300m/min and finished the race one miute faster than he had during training. What distance was the race?
Answer:
6 m
Step-by-step explanation:
First I want you to understand that distance = speed × time.Consider:
speed= 250. 300.
minutes= let it be x. x-1
distance= 250× x. 300(x-1)
=250x. 300x-300
Since distance remains the same ,250x=300x-300
hence. -50x=-300.
x= 6
The length of the race was 1500 meters.
What is Speed?
Speed is defined as the rate of change of distance travelled per unit time.
Given is an athlete who ran at a speed of 250 m/min. However, on the day of the race, he increased his average speed to 300 m/min and finished the race one minute faster than he had during training.
Assume that the length of the race is (x) meters. Suppose that the runner takes (t) minutes to to complete the race in training. Therefore, we can write -
x = 250t
During the race -
x = 300(t - 1)
Equating both, we get -
250t = 300(t - 1)
250t = 300t - 300
300 = 50t
t = 6 min
Then, the length of the race will be -
x = 250 x 6 = 1500 meters
Therefore, the length of the race was 1500 meters.
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A total of 290 people attended the high school play. The admission prices were $14 for adults, $7 for high school students, and $3 for children not yet in high school. The ticket sales totalled $2040 The principal suggested that next year they raise prices to $17 for adults, $8 for high school students, and $4 for children not yet in high school. He said that if exactly the same number of people attend next year, the ticket sales at the higher prices will total $2470
How many adults, high school students, and children not yet in high school attended this year?
The number of adults, high school students, and children not yet in high school attended this year are respectively; 70, 100, 120
How to solve a system of simultaneous equations?We are told that a total of 290 people attended the high school play.
If x represents number of adults, y represents number of high school students and z represents number of children, then we have;
x + y + z = 290 ---- (1)
The admission prices were $14 for adults, $7 for high school students, and $3 for children not yet in high school. The ticket sales totaled $2040 . Thus;
14x + 7y + 3z = 2040 ---- (2)
The principal suggested that next year they raise prices to $17 for adults, $8 for high school students, and $4 for children not yet in high school. Total cost of $2470. Thus;
17x + 8y + 4z = 2470 ---- (3)
Solving the three equations simultaneously gives;
x = 70, y = 100, z = 120
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What is the product in simplest form?
-8/9 . 5/6
516
O-1
O
T
35
15
20
27
16
The value of the product -8/9 . 5/6 is -20/27. Option C
What is a fraction?A fraction can simply be defined as the part of a whole set or element.
The several types of fractions are listed as;
Simple fractionsComplex fractionsProper fractionsImproper fractionsMixed fractionsExamples of proper fractions: 3/4, 5/6
Examples of improper fractions: 4/3 , 8/7
Examples of mixed fractions: 2 1/2 , 3 4/5
Examples of simple fractions: 1/2 , 1/3
Given the expression:
-8/9 . 5/6
To determine the product of the fractions, we need to follow the steps
Multiply the numerators
-40/ 9 × 6
Now, multiply the denominators
-40/57
Reduce to simplest forms by using the divisor 2, we have;
-20/ 27
Hence, the value is -20/27
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A sandwich store charges $20 to have 3 turkey subs delivered and $26 to have 4 delivered.
Is the relationship between number of turkey subs delivered and amount charged proportional? Explain how you know. (Proportional just means equal)
A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four. There is no proportionality between the quantity of turkey subs delivered and the amount billed.
Given that,
A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four.
We have to find the relation ship between the quantity of turkey subs delivered and the amount billed.
The reciprocal of the ratio of subs to amount charges is
We get,
3/20 and 4/26
Since,
3/20≠4/26
Therefore, There is no proportionality between the quantity of turkey subs delivered and the amount billed.
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Kinsley's house is due west of summerfield and due south of hillsdale. summerfield is 6 kilometers from kinsley's house and 10 kilometers from hillsdale. how far is hillsdale from kinsley's house, measured in a straight line?
The Hillsdale is 8 km from the Kinsley's house
Let Kinsley's house be A
Summerfield be B
Hillsdale be C
The Kinsley's house due west of Summerfield be AB which is 6 km and The distance between Summerfield and Hillsdale is BC which is 10 km
Distance between Kinsley's house and Hillsdale can be calculated using Pythagoras' theorem, which states that the square of the hypotenuse is equal to the sum of the square of the other two sides.
BC² = AB² + AC²
We need AC, so let us rewrite this equation
AC² = BC² - AB²
AC² = 10² - 6²
AC² = 100 - 36
AC² = 64
AC = √64
AC = 8 km
Therefore, Kinsley's house is due south of Hillsdale from 8 km
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3. a 95% confidence interval for a slope spans from 10 to 20, but the level of confidence changes to 99%, list a plausible 99% confidence interval for the new slope
( 8.43 , 21.57) is ist a plausible 99% confidence interval for the new slope.
In algebra, what is an interval?
In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number you may imagine is a real number.95% of confidence interval = (10 ,20)
x = 10 + 20 /2 = 15
margin of error = 20 - 10 /2 = 10/2 = 5
SE = Margin of error/2 = 5/1.96 = 2.551
99% confidence interval = x ± z/2 * 3E
= 15 ± 2.576 * 3E.
= 15 ± 2.576 * 2551
= 15 ± 6.571376
= (15- 6.571376 , 15 + 6.571376)
= ( 8.43 , 21.57)
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if b=5, what is b^3=
Answer:
15
Step-by-step explanation:
B*3
5*3
15
Answer:
Step-by-step explanation: if b= 5 the the equation will be (5)^3 you multiply and get 15
Which equation has the same solution as 4-(2x-5)= (x-19)/4
Algebric equations which has the same solution as 4 - 2(x - 5) = (x - 19)/4 are all equations which has a solution of 55/9.
The equation given is,
4 - (2x-5) = (x - 19)/4
16 - 4(2x - 5) = (x - 19)
16 - 8x + 20 = x - 19
All terms having a variable x is taken to one side and the numerical values are kept on the other side.
16 + 20 + 19 = x + 8x
9x = 55
x = 55/9
Therefore, equation which has the same solution as 4 - 2(x - 5) = (x - 19)/4 are all equations which has a solution of 55/9.
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As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.
As the sample size becomes larger, the sampling distribution of the sample means approaches a sampling distribution.
What is sampling distribution?Regardless of the distribution of the population one samples from, is roughly normally distributed for a large sample size (we shall explain this later). The population will have a mean and standard deviation if it has a mean and one.Regardless of the distribution of the population, the central limit theorem (CLT) states that the distribution of sample means approaches a normal distribution as the sample size increases. The CLT is frequently thought to hold for sample sizes equal to or larger than 30.The sample size and variability affect how accurate your statistics are. A tighter confidence interval with a smaller margin of error will be obtained with a bigger sample size or lower variability.Therefore, as the sample size becomes larger, the sampling distribution of the sample means approaches a sampling distribution.
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Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A.
all of the measurement pairs that could be the dimensions of Rectangle B.
When Rectangle A measures 9 inches by 3 inches and rectangle B is a scaled copy of Rectangle A, the possible dimensions will be:
3 inches by 1 inches6 inches by 2 inchesHow to express the value?From the information, Rectangle A measures 9 inches by 3 inches. Therefore, the ratio will be:
=Length / Width
= 9 / 3
= 3:1
Therefore, a scaled copy will have an equivalent ratio of 3:1.
This can be 3 inches by 1 inches and 6 inches by 2 inches. Their ratio is:
= 6/2 = 3:1.
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The perimeter is 70cm2. The sides are 3x-1, 3x, 4x+ 1. What is x?
The perimeter is 70[tex]cm^{2}[/tex]. and x is 7
What is perimeter ?The complete circumference of a shape is referred to as its perimeter. It is the length of any geometric shape with a two-dimensional boundary or outline. Depending on their proportions, multiple figures can have equal perimeters. Think of a triangle built of an L-length wire as an example. If the length of each side is the same, the same wire can be used to create a square. Look at the illustration below, which shows the bounds of a rectangular park.
Given that :The perimeter is 70[tex]cm^{2}[/tex]. The sides are 3x-1, 3x, 4x+ 1.
3x -1 + 3x + 4x + 1 = 70
10x = 70
x = 7
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TV
and
WY
areparallellines.
S
T
U
V
W
X
Y
Z
Which angles are adjacent angles?
Since TV and WY are parallel lines, the angles which are adjacent angles include the following: C. <VUX and <WXZ.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is the vertical angles theorem?The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
In Geometry, when two (2) parallel lines are cut by a transversal, the vertical angle and its adjacent angle that are formed are supplementary angles, which makes:
<VUX and <WXZ.
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Complete Question:
TV and WY are parallel lines. Which angles are adjacent angles?
<VUX and <TUX.
<VUX and <VUX.
<VUX and <WXZ.
<VUX and <YXZ.
12. The sales tax rate in a certain state is 6%.
Find the total price paid for a pair of pants
that costs $44.
Answer:
$46.64
Step-by-step explanation:
convert 6% to .06
multiply that by 44
you get 2.64.
add that to 44 to get a final ansewr of 46.64 dollers
The height, h, in meters, of a falling object is related to the time, t, in seconds, the object
has been falling, by the formula h= -4.9t² + d, where d is the initial height, in meters, of
the object above the ground. If an object is dropped from a height of 32 meters, how long
does it take the object to hit the ground? Round the answer to the nearest hundredth of a second.
The amount of time it would take this object to hit the ground is 2.56 seconds.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
What is the maximum value of a function?The maximum value of a function can be defined as a point on the graph where the function reaches its highest point. This ultimately implies that, the maximum value of a function simply refers to its vertex on a graph.
The height (h) in meters, of this falling object is related to the time by the following function:
h = -4.9t² + d
Substituting the given parameters into the formula, we have;
0 = -4.9t² + 32
4.9t² = 32
Time, t² = 32/4.9
Time, t² = 6.53
Time, t = √6.53
Time, t = 2.56 seconds.
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Given: A, B, and C are collinear, AB=BD, and BD=BC
Prove: B is the midpoint of AC
Using the definition of a midpoint and collinear points, the proof that shows that B is the midpoint of AC is explained below.
What are Collinear Points?If three points are on a straight line, they are defined as being collinear points. That is, three points, A, B, and C are collinear points if they are on a straight line, and B is in the middle of points A and b.
What is the Midpoint of a Segment?When a segment is divided into two equal halves, the point that lies in the middle of the segment where the segment is cut into halves is called the midpoint of the line segment.
The proof that shows that B is the midpoint of line segment AC is shown below:
Statements Reasons
a. A, B, and C are collinear a. Given
AB = BD, BD = BC
b. AB = BC b. Substitution
c. AB ≅ BC c. Definition of congruency
d. B is the midpoint d. AB ≅ BC
Thus, the proof above explains how point B is the midpoint of line segment AC in the image given.
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Express x2-5x + 8 in the form (x-a)² + b
where a and b are top-heavy fractions.
Using Complete the Square method, we find out that [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.
It is given to us that the expression is -
[tex]x^{2} -5x+8[/tex] ----(1)
We have to express it in the form of[tex](x-a)^{2}+b[/tex] where a and b are top-heavy fractions.
In order to achieve the required expression in the form of [tex](x-a)^{2}+b[/tex] we have to use "Completing the Square" method.
The given expression from (1) is -
[tex]x^{2} -5x+8[/tex]
This expression is in the form of [tex]ax^{2} +bx+c[/tex]
Adding and subtracting [tex](b/2)^{2}[/tex] terms into the expression, we get
[tex]x^{2} -5x+[\frac{5}{2}] ^{2}-[\frac{5}{2}] ^{2}+8[/tex] -----(2)
Equation (2) can also be represented as -
[tex](x-\frac{5}{2}) ^{2} -[\frac{5}{2}] ^{2} +8[/tex]
[tex]= > (x-\frac{5}{2}) ^{2} -\frac{25}{4} +8\\= > (x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex]------- (3)
We see that equation (3) is in the form of [tex](x-a)^{2}+b[/tex].
So, we can derive that -
[tex]a=\frac{5}{2}[/tex]
and, [tex]b=\frac{7}{4}[/tex].
Thus, [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] through "Complete the Square" method as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.
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Use the image above to identify and explain the relationship between the segments and circles A and B. In your explanation, be sure to include specific vocabulary and definitions for the relationships.
PS
Circle A and Circle B's connection
Circle A's size is more significant than Circle B's size.
As a result, circle A's radius exceeds circle B's radius.
The connection between segments
1.
Let M be the location where Segment QT and ER intersect.
Additionally, tangents from an outside point to a circle have identical lengths.
QM = ME———— (1)
MT=MR————(2)
Including (1) and (2)
MR + ME = QM + MT
Q T=ER
2.
Tangents from an exterior point to a circle have identical lengths.
We may write the following segments are equal using this property.
UP=U Q
ZC=ZR
VC=VS
NR=NS
KC=K T
What are Tangents?
A line that only touches a circle or an ellipse at one point is said to be divergent in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve. The following methods can be used to find the tangent equation in differential geometry:
As we are aware, the gradient of the curve at any given location on the curve is equal to the gradient of the tangent to the curve. The following is how to determine the tangent equation of the curve y = f(x):
Utilizing the differentiation principles, determine the gradient function's derivative.
To determine the tangent's gradient, the derivative should be changed to include the provided point's x-coordinate
Find the tangent equation by substituting the provided coordinate point and the gradient of the tangent into the straight-line equation (in a slope-point formula).
Circle's Tangent
A closed, two-dimensional form, a circle is also a curve. The radius of the circle or the line from the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying picture.
Geometric Tangent
Here, "AB" stands for the tangent, "P" for the point of tangency, and "O" for the circle's center. The OP is the radius of the circle.
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Leily was guessing Joseph’s number. He said that his number was composite, even, and a square number between 15 and 30. What is Joseph’s number?
The number that Joseph is thinking of that is between 15 and 30 is 16.
What is Joseph’s number?The first step is to determine the squares between 15 and 30. The square of a number is the product of a number with itself. For example, 16 is a square number.
Squares between 15 and 30 = 16, 25
The next step is to determine the even number. An even number is a number that is perfectly divisible by 2. An example of an even number is 4.
The even number that is a square between 15 and 30 is 16.
The last step is to determine the composite number. A composite number is a number that has more than 2 factors.
Factors of 16 = 1, 2, 4, 8, 16
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Function g is a transformation of the parent function f(x) = x2. The graph of g is a translation left 4 units and down 2 units of the graph of f.
Write the equation for g in the form y = ax2 + bx + c.
f(x) = x^2
write new equation after translation using vertex form;
(x+4)^2 - 2
simplify; convert to standard form
(x+4)(x+4) - 2
x^2 + 8x - 2
The function after translation is g(x) = x²+ 8x - 2.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given:
f(x) = x²
Now, g is a translation left 4 units and down 2 units of the graph of f.
So, g(x)= (x+4)² - 2
Then, in the standard form
g(x) = (x+4)(x+4) - 2
g(x) = x²+ 8x - 2
Hence, the function is g(x) = x²+ 8x - 2.
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A kangaroo hops 2 kilometers in 3 minutes. At this rate, how long, in minutes, does it take the kangaroo to hop 5 kilometers? Answer ________________________ minutes At this rate, how far, in kilometers, does the kangaroo travel in 2 minutes? Answer ________________________ kilometers
Answer:
It takes the kangaroo 7.5 minutes to travel 5 kilometers.
Step-by-step explanation:
It takes the kangaroo 7.5 minutes to travel 5 kilometers.
First step is to formulate
3×5/2
Second step is to determine the time by calculating the product or quotient
Time=3×5/2
Time=15/2
Time=7.5 minutes
Inconclusion how long it takes the kangaroo to travel 5 kilometers is 7.5 minutes.
50pts for this question:)
Answer: 1: 6√6 = 36
hope this helps, good luck!
Please hellllp
Determine the intercepts of the line.
Do not round your answers.
4x1= 3y + 5
x-intercept:
y-intercept:
Answer: x-intercept: 5/4
y-intercept: -5/3
Step-by-step explanation:
We can find the y-intercept by looking at the y = mx + b form, the y-intercept would be b in that form:
4x = 3y + 5
y = 4/3x - 5/3
Next, we plug x into that equation:
We can graph it, or find it mathematically:
Set 4/3x = 5/3
4/3x * 3/4 = 5/3 * 3/4
x = 5/4
A 10-visit movie pass costs $79.50. What is the unit rate for each visit
Answer:
$7.95 per visit
Step-by-step explanation:
To find the unit rate, divide dollars by number of visits.
79.5 ÷ 10 = 7.95
A kite is at the end of a string that is 40 meters long. The person
is holding the end of the string 3 meters off the ground, and the
angle of elevation formed by the string is 50°. Which expression
represents how high in meters the kite is off the ground?
The expression representing height of kite from ground is Height = sin 50° × 40.
The kite, person holding the string and ground from where height is to be measured will form right angled triangle. We can use the sine function to find the height of kite from the ground. Writing the trigonometric relation -
sin theta = perpendicular ÷ hypotenuse
Keep the values in mentioned trigonometric relation to find the expression -
sin 50 = height ÷ 40
Height = sin 50° × 40
Finding the height using formed equation -
Height = 0.77 × 40
Performing multiplication
Height = 30.64 meters
Therefore, the expression to find the height of kite from ground is Height = sin 50° × 40.
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Convert 180 pounds to kilograms
Answer:
"What is 180 lbs to kg?" is the same as "What is 180 pounds to kilograms?" or "What is 180 pounds to kg?" or "What is 180 lbs to kilograms?" Here we will show you how to convert 180 lbs to kg.
There are 0.45359237 kilograms per pound and there are 2.204622622 pounds per kilogram. Therefore, you can get the answer to "180 lbs to kg?" two different ways. You can either divide 180 by 2.204622622 or multiply 180 by 0.45359237. Therefore, the answer is
Step-by-step explanation:
81.6466
suppose a series system has three components c1, c2, and c3 with the probability that each component functions equal to 0.90, 0.99, and 0.95, respectively. what is the probability that the system operates? (4 decimals)
0.8465 is the probability that the system operates if the probability that each component functions equals to 0.90, 0.99, and 0.95 respectively.
As the components are in a series system, this means that all the components have to function in order for the system to operate, and the failure of any one of the components to function will result in the system not operating.
Therefore, the probability for the system to operate is the probability that all the components c1, c2, and c3 function together
The probability of multiple events occurring together can be found by multiplying the probabilities of each event by one another.
Therefore;
Probability = 0.90 × 0.99 × 0.95
Probability = 0.84645
Rounding it off to 4 decimals as follows;
Probability = 0.84645 = 0.8465
Therefore, the probability that the system operates is calculated to be 0.8465.
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calculate the volume of air in liters that you might inhale (and exhale) in 8.00 hours. assume that each breath has a volume of 0.475 liters, and that you are breathing 18 times a minute.
The volume of air in liters that might inhale (and exhale) in 8.00 hours is 4060.8 litres.
What is defined as the unitary method?The unitary method is one that involves determining the value of a single unit and then calculating the value of a required number of units based on that value.The unitary method's formula is to identify the value of a specific unit and then multiply that value by the number of units to arrive at the required value.For the given question;
The volume of air inhale (and exhale) once = 0.475 liters
Number of breathing in 1 minutes = 18 times.
Thus, the volume of air inhaled in 1 minutes is 0.47×18 = 8.46 litres.
This can be written as;
1 minutes ------- > 8.46 litres of air.
For calculating in 8 hours that is 8×60 = 480 minutes, multiply the both side by 480 in above equation;
1× 480 minutes ------- > 480×8.46 litres of air.
480 minutes --------> 4060.8 litres of air.
Therefore. the volume of air in liters that might inhale (and exhale) in 8.00 hours is 4060.8 litres.
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exclude leap years from the following calculations. (a) compute the probability that a randomly selected person does not have a birthday on december 9. (b) compute the probability that a randomly selected person does not have a birthday on the 3rd day of a month. (c) compute the probability that a randomly selected person does not have a birthday on the 30th day of a month. (d) compute the probability that a randomly selected person was not born in february.
Answer:
yes
Step-by-step explanation:
Goggle
I need help!!! I’m taking a test that might feasible my grade
Answer:
you'll need a graph to answer this
Four teenage, who all work at the same rate, can clean a house in 6 hours. How long would it take three of them to clean the same hose.
If 4 teenagers can clean in 6 hours, 1 teenager will take 4x more time
1 teenager will take 24 hours = k
No. of teenagers (p) is proportional to time (t):
p = k/t
3 = 24/t
t = 24/3 = 8 hours
So it will take 8 hours for 3 teenagers to clean a house.
8 hours
Step-by-step explanation:
teenagers. hours
4. 6
3. ?
it is actually direct multiplication where you multiply the upper numbers,4 × 6 ,then divide by the lower value, 3. This gives 24 /3 which gives you 8 .