Answer:
There are 3 groups that need to cross a river and each boat can only carry 1/3 of a group. How many boats are there needed to get everybody across
Step-by-step explanation:
The Euclid's division lemma is used to find the HCF of two numbers. The given result has been represented in word problem in detail.
What is Euclid's division lemma?Euclid's division lemma can be written in mathematical form as
A = QB + R, where a number P divided by number s gives a quotient Q and a remainder R.
It is applicable both to numbers and algebraic expressions.
Given that,
The quotient is 3,
And, the divisor is 1 / 3.
The given results can be represented in the form of a word problem as follows,
John has a piece of land which he wants to divide in three equal parts. To how many persons he can distribute his land?
Hence, the given results can represented in the form of a word problem as mentioned above.
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Find the indicated probability. Round to three decimal places.
A car insurance company has determined that 7% of all drivers were involved in a car accident last year. Among the 19 drivers
living on one particular street, 4 were involved in a car accident last year. If 19 drivers are randomly selected, what is the
probability of getting 4 or more who were involved in a car accident last year? (Hint: use binomial probability).
Answer:
explanation below
Step-by-step explanation:
so in order for all 19 drivers to not be in a car accident the probability is
.93 ^ 14 which is around 0.362,
next for 18 of the drivers no accident its
.93^13 x .07 x 19 = around .518
for 17 drivers,
.93^12 x .07^2 x 171 = around .350
for 16 drivers,
so on and you can do the rest
A football team loses 2 yards every 5 minutes. How many yards did the team lose after 15 minutes?
How much will a person pay for 11.6 pounds of bananas at a price of 1.51 per pound?
Answer:
17.52
Step-by-step explanation:
literally 11.6 x 1.51 and then round to hundredth place
Question 9 of 10
$10,000 is compounded semiannually at 12% interest for t years. What
expression represents the amount of money after t years?
A. $10,000(1+0.12)^t
B. $10,000(1+0.12/2)^2t
C. A$10,000(1+0.12/4)^4t
D. $10,000(1+0.12)^12t
Answer:
A
Step-by-step explanation:
Answer:b
Step-by-step explanation:
a coffee company wants a new flavor of Cajun coffee. how many pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound?
24 pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound.
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given situation:
A coffee $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound
Now, Let x be the amount of coffee which is $10 per pound
So,
10x + 3(30) = 5(x+30)
10x + 30 = 5x+150
5x + 30 = 150
5x = 120
x = 24 pounds
Hence, 24 pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound.
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Solve in any method. Help please
#3 Preimage point B is
located at (5,-4).
B' is located at (20, -16).
Write the algebraic rule for
the transformation.
The algebraic rule for the transformation is B' = (Bx + 15, By - 12)
Given data ,
To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.
Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:
B' = (Bx + dx, By + dy)
Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:
dx = 20 - 5 = 15
dy = -16 - (-4) = -12
Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)
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Trigonometry
Ineach of the questions below, calculate other the missing angle or side stated. Give
your answer correct to 1 decimal place
1)
3)
13cm
39m
38
4cm
10m
14m
6)
140m
9)
5cm
2)
4)
23m
75m
10cm
35"
7)
16m
10)
d
6cm
66°
135m86
15m
Answer: Ans(1)
In right triangle
a = 13cos(56°)
a = 7.3 cm
Ans(2)
In right triangle
b = 6/sin(35°)
which missing number makes the following exlression equivalent 8(3x -5) ____ x _____ please explain????
Answer:
24x-40
Step-by-step explanation:
you use the distributive property to distribute 8 to 3x and -5
3x(8)= 24x and -5(8)= -40
When a bottle of milk replacer is made we add 1 cup of powdered milk to a 12 qt bottle. What is the ratio of powder to water?
Answer:
approximately 4 Tbsp. of powdered milk to 1 cup of water
Step-by-step explanation:
Answer:
....................
Find the length of the hypotenuse.
a. 12
b. 6
c. 5
d. 18
Answer:
B. 6Step-by-step explanation:
1) Take sin45
2) sin45= 3√2/ x
3) 3√2/sin45
4) x=6
Where x = hypotenuse
and sin 45 is opposite over adjacent
2 points
11. (24.7D) The synthetic division problem shown below
can correctly be represented by which
statement(s)?
2] 3 -10
6
3 -4
10 -4
-8 4
2 0
I.
II.
One factor is (x - 2)
One factor is (x + 2)
One factor is (3x2 - 4x + 2)
One factor is (3x3 – 4x2 + 2x)
III.
IV.
A. IV only
B. III Only
C. I and III
D. I and IV
Answer:
C. I and III
Step-by-step explanation:
The 2 at the upper left means the divisor is x - 2.
The result at the bottom means the quotient is 3x^2 - 4x + 2.
Answer: C. I and III
Question 3
A group of 5 people went to the movies and spent $44 on food and drink. The total amount spent, including
tickets, was $98.50.
What was the price, in dollars, of one ticket?
Answer:
One ticket cost $10.90.
Step-by-step explanation:
The total spent was $98.50--food, drinks, admission--everything.
$44.00 was for food and drinks.
We can take the 44 away from the total.
98.50 - 44.00
= 54.50
They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.
54.50 ÷ 5 = 10.90
The price of one ticket was $10.90
To make this look like algebra class...
let x = the price of one ticket
5x = the price of 5 tickets
5x + 44 = 98.50
subtract 44
5x = 54.50
divide by 5
x = 10.90
You sailed 0.055 units to the left and found treasure at 0.085 units find where the ship started
For many important processes that occur in the body, direct measurement of characteristics of the process is not possible. In many cases, however, we can measure a biomarker, a biochemical substance that is relatively easy to measure and is associated with the process of interest. Bone turnover is the net effect of two processes: the breaking down of old bone, called resorption, and the building of new bone, called formation. A biomarker for bone formation measured was osteocalcin (OC), measured in the blood. The units are nanograms per milliliter (ng/ml). For the 31 subjects in the study the mean was 33.4 ng/ml. Assume that the standard deviation is known to be 19.6 ng/ml.
Required:
Give the margin of error and find a 95% confidence interval for the mean TRAP amount in young women represented by this sample.
Answer:
The margin of error is \(E = 6.9 \)
The 95% confidence interval is \( 26.5 < \mu < 40.3 \)
Step-by-step explanation:
From the question we are told that
The sample size is n = 31
The mean is \(\mu = 33.4 \ ng/ml\)
The standard deviation is \(\sigma = 19.6 \ ng/ml\)
From the question we are told the confidence level is 95% , hence the level of significance is
\(\alpha = (100 - 95 ) \%\)
=> \(\alpha = 0.05\)
Generally from the normal distribution table the critical value of \(\frac{\alpha }{2}\) is
\(Z_{\frac{\alpha }{2} } = 1.96\)
Generally the margin of error is mathematically represented as
\(E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }\)
=> \(E = 1.96 * \frac{19.6 }{\sqrt{31 } }\)
=> \(E = 6.9 \)
Generally 95% confidence interval is mathematically represented as
\(\= x -E < \mu < \=x +E\)
=> \( 33.4 - 6.9 < \mu < 33.4 + 6.9 \)
=> \( 26.5 < \mu < 40.3 \)
what is the mathematical expression of “the sum of a number x and three”
Answer: X + 3
Step-by-step explanation:
Sum hints as to an addition statement and it specifies a variable X and the number 3 so the expression would be X + 3.
SUM MEANS ADDITION
HERE IT MEANS THE ADDITION OF x and 3
written as
\(x + 3\)
HOPE THIS HELPS
A girl sold a bike for $ 24, which was 1/4 less than she paid for it. How much did she pay for the bicycle?
The girl paid for the bicycle is $32
How to calculate how much the girl paid for the bicycle?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator
Given that: the girl sold the bike for $ 24, which was 1/4 less than she paid for it.
Let P represent the amount she paid for the bicycle
This can be written as:
P- (1/4)P = 24
3/4 P = 24
P = (24 × 4)/ 3
P = 96/3
P = 32
Therefore, the amount she paid for the bicycle is $32
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At a party, there are 40 children and 20 adults.What fraction shows the ratio of children to the total number of people at the party?A.20/40B.40/20C.40/60D.60/40
no of total people is children + adults = 40 + 20
the fraction is = no. of children/ no. of total people
= 40 / (40 + 20 )
= 40 /60
thus, the correct answer is option C
2. If JKLM is a rhombus, MK = 30, NL = 13, and m/MKL = 41°, find each measure.
3. If WXYZ is a square with WZ = 27, find each measure.
The measure of YZ = 27
WY = 27√2
RX = 27/2 √2
and <XYZ = <ZWY = < WRZ= 90°
What are the properties of a square?A square is a quadrilateral with all the sides and angle equal. This are some of the properties of a square;
1. All four interior angles are equal to 90°
2. All four sides of the square are congruent or equal to each other.
3. The opposite sides of the square are parallel to each other.
4. The diagonals of the square bisect each other at 90°
5. The two diagonals of the square are equal to each other.
since a sides are equal,
YZ = 27
using Pythagoras
WY² = 27²+27²
WY = √1458
WY = 27√2
RX = WY/2
RX = 27/2 √2
and
XYZ = <ZWY = < WRZ= 90°
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What does the net decimal equivalent (NDE) represent?
Answer:
the product of the decimal equivalents of all discount in the series
an air traffic controller is tracking two planes. to start plane A is at the altitude of 4000 feet and plane B is at an altitude of 3146 feet. plane A is gaining altitude at 33.5 feet per second and plane B is gaining altitude at 50.75 feet per second
the two planes will be at the same altitude of approximately 5675.48 feet after 49.45 seconds.
What is plane?A plane is a flat two-dimensional surface that extends infinitely in all directions. In geometry, a plane is defined as a surface that is completely flat and has no thickness. It is often represented as a coordinate system with two perpendicular axes, usually labeled as the x-axis and y-axis.
Assuming that the two planes maintain their rates of ascent, we can use the following equations to determine when the planes will be at the same altitude:
altitude of plane A = 4000 + 33.5t
altitude of plane B = 3146 + 50.75t
where t represents time in seconds.
To find the time at which the two planes will be at the same altitude, we can set the two equations equal to each other and solve for t:
4000 + 33.5t = 3146 + 50.75tSubtracting 3146 from both sides, we get:
854 + 33.5t = 50.75t
Subtracting 33.5t from both sides, we get:
854 = 17.25t
Dividing both sides by 17.25, we get:
t = 49.45 seconds
Therefore, it will take approximately 49.45 seconds for the two planes to be at the same altitude. To find the altitude at which they will meet, we can substitute this value of t into either equation. Using the equation for plane A, we get:
altitude of plane A = 4000 + 33.5(49.45) = 5645.08 feet
Using the equation for plane B, we get:
altitude of plane B = 3146 + 50.75(49.45) = 5675.48 feet
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Which statement is true about the graphed function
Grandma Bunga is 52 years older than Melati. She is 5 times older than Melati. How old
is Grandma Bunga?
Answer:
65
Step-by-step explanation:
x=52+y
x=5y
y=x/5
x=52+(x/5)
x-(x/5)=52
(5x-x)/5=52
4x=52×5
4x=260
x=260/4
x=65
Bunga is 65 yrs old
Metali is 13 yrs old
Sketch and label a net of the right triangular prism. Each square on the grid represents
1 square centimeter. Calculate the surface area of the prism by using its net.
The total surface area of the prism is determined as 216 cm².
What is the surface area of the prism?The surface area of the prism is calculated by applying the following formula.
The area of the two triangular faces is calculated as follows;
Area of the two triangles = 2 (¹/₂ x base x height )
Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )
Area of the two triangles = 24 cm²
The area of rectangular faces is calculated as follows;
A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )
A = 192 cm²
The total surface area of the prism is calculated as follows;
Area = 24 cm² + 192 cm²
Area = 216 cm²
The sketch of the triangular prism is in the image attached.
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a. Write an inequality that represents the numbers that are not solutions of x+3.8>11.3 .
Inequality:
Question 2
b. Graph the inequality from part (a).
Inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.
What are the various operators used in inequalities for comparison?The various operators used in inequalities for expression are -
greater than - ' > 'less than - ' < 'greater than or equal to - ' ≥ 'less than or equal to - ' ≤ 'Given is a inequality in one variable which is → x + 3.8 > 11.3.
PART - A
The inequality that represents the coordinates that are not the solutions of this inequality is -
x + 3.8 < 11.3
or
we can simplify it to get -
Subtract 3.8 from both sides -
x + 3.8 - 3.8 < 11.3 - 3.8
x < 7.5
PART - B
In order to plot the graph of this inequality, firstly we will plot the line of equation -
x = 7.5.
Since, the inequality is strict, make a dashed line to represent the equation.
Take the coordinates of origin O(0,0), and substitute it in the inequality -
0 < 7.5
which is true. Therefore, we will shade the complete side where origin lies.
The graph of the inequality is plotted an attached with the answer.
Therefore, inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.
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16 2/3 is the same as
1. Convert the fraction to a decimal: Divide the numerator by the denominator
2. Add this decimal number to the whole number part of the mixed number
Which expression has a value that is equivalent to 5n + 13 when n=−5?
Answer:
-25+13 answer is -12
Step-by-step explanation:
Thirty-two different video games showing drug use were observed. The duration times of drug use (in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 82 sec, what does df denote, and what is its value? What does df denote?
A. The sample size
B. The test statistic
C. The sample standard deviation
D. The number of degrees of freedom
The value of df is _________ Type an integer or a decimal. Do not round )
Answer:
D. The number of degrees of freedom
The value of df is 31
Step-by-step explanation:
Degrees of freedom (DF) denotes the amount of information provided by the data you can "consume" to estimate unknown population parameters' values and calculate the variability of those estimates.
Increasing the sample size provides more information about the population, which increases the degrees of freedom present in the data.
Given that:
The sample size in the study (n) = 32
The degree of freedom df = n - 1
The degree of freedom df = 32 - 1
The degree of freedom df = 31
Which term can be added to the list so that the greatest common factor of the three terms is 12h3?
36h3, 12h6, __________
The term that can be added to the list so that the greatest common factor of the three terms 12h3 36h3, 12h6, is 48h5
How can the term be known?A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.
The term that can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12 without any fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.
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Use rounding (to the nearest 10) to estimate the product of 3217 x 44.
Answer:
141,548
Step-by-step explanation:
the product means you need to multiply