Answer:
B. 10/2, E. 6.3
Step-by-step explanation:
First, you need to solve for x by isolating it on one side of the inequality. You can do this by adding 3 to both sides and then dividing by 2:
2x - 3 > 1
2x - 3 + 3 > 1 + 3
2x > 4
2x / 2 > 4 / 2
x > 2
Next, you need to find two numbers that are greater than 2 and plug them into the inequality to check if they make it true. You can choose any numbers that are larger than 2, but it is easier to pick from the given options. For example, let’s try A. 3/2 and B. 10/2:
A. x = 3/2
2(3/2) - 3 > 1
3 - 3 > 1
0 > 1, False
B. x = 10/2
2(10/2) - 3 > 1
10 - 3 > 1
7 > 1, True
Then, you need to repeat the same process for the remaining options until you find another number that makes the inequality true. For example, let’s try C. 1, D. 2, and E. 6.3:
C. x = 1
2(1) - 3 > 1
2 - 3 > 1
-1 > 1 False
D. x = 2
2(2) - 3 > 1
4 - 3 > 1
1 > 1, False
E. x = 6.3
2(6.3) - 3 > 1
12.6 - 3 > 1
9.6 > 1, True
Finally, you need to select the two numbers that make the inequality true from the options. The answer is B. and E. B. 10/2 and E. 6.3 are two numbers that make the inequality true.
There are 10% more boys than girls in a choir. If there are 4 more boys than girls, how many children are there altogether?
Step-by-step explanation:
There are 10% more boys than girls in a choir.
b = 1.1g
If there are 4 more boys than girls,
b = g + 4
Replace b with 1.1g
1.1g = g + 4
1.1g - g = 4
.1g = 40
g = 4/.1
g = 40 girls, then + 4 = 44 boys
anushka and arushi are friends. they have equal amount of money. anushka gives arushi 1/3 as a gift. then arushi spends half of her total money, if the money arushi has left is 1600 then whats the amount gifted to arushi. give answer with steps
Answer: Rs. 3200
Step-by-step explanation:
Let's assume the amount of money they both had before Anushka gives Arushi a gift as "M".
After Anushka gives Arushi 1/3 of her money, Arushi has 1/3 of Anushka's money, which is (1/3)×M.
Then, Arushi spends half of her total money, which means she spends (1/2)×[(1/3)×M] = (1/6)×M.
So now Arushi has (1/3)×M - (1/6)×M = (1/6)×M left.
According to the problem statement, (1/6)×M is equal to 1600. So we can set up an equation:
(1/6)×M = 1600
Multiplying both sides by 6, we get:
M = 9600
So the total amount of money they both had initially was Rs. 9600.
We know that Anushka gave 1/3 of this money to Arushi, which is:
(1/3)×9600 = 3200
Therefore, the amount gifted to Arushi was Rs. 3200.
The product of two numbers is 155952. If one number is 342, find the other
number.
The other number is 456.
Given that the product of two numbers is 155952, one number is 342, we need to find the other number.
So, let the other number be x,
Therefore, x × 342 = 155952
x = 155952 / 342
x = 456
Hence the other number is 456.
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9/18 is equivalent to which fraction
Answer: 1/2 simplest form
Step-by-step explanation: 9 is half of 18 so the smallest fractions that is equivalent to 9/18 is 1/2.
Your gross income is $4,520.00/month. Your deductions are FICA (7.65%), federal tax withholding (11.75%), and state tax withholding (8.5%). Your fixed expenses are 30% of your realized income. You saved 5 months' worth in an emergency fund, placing 75% in a 60-day CD at a 5.25% APR and the rest in a regular savings account at a 3.8% APR. How much is the total interest earned between both accounts in 60 days?
a)$44.31
b)$59.06
c)$39.27
d)$41.19
Answer:
C
Step-by-step explanation:
First, we need to calculate the net income after deductions:
FICA = 7.65% x $4,520.00 = $346.38
Federal tax withholding = 11.75% x $4,520.00 = $531.40
State tax withholding = 8.5% x $4,520.00 = $384.20
Total deductions = $346.38 + $531.40 + $384.20 = $1,262.98
Net income = $4,520.00 - $1,262.98 = $3,257.02
Next, we need to calculate the amount allocated for fixed expenses:
Fixed expenses = 30% x $3,257.02 = $977.11
The remaining amount that is available for savings is:
Savings = $3,257.02 - $977.11 = $2,279.91
The emergency fund is equal to 5 months' worth of fixed expenses, which is:
Emergency fund = 5 x $977.11 = $4,885.55
The amount placed in the CD is 75% of the emergency fund, which is:
CD = 75% x $4,885.55 = $3,664.16
The amount placed in the regular savings account is:
Savings account = $4,885.55 - $3,664.16 = $1,221.39
To calculate the interest earned in the CD in 60 days, we use the formula:
Interest = Principal x Rate x Time
where the rate is annual percentage rate (APR) divided by 365 (number of days in a year)
Interest earned in the CD = $3,664.16 x (5.25%/365) x 60 = $21.97
To calculate the interest earned in the regular savings account, we use the formula:
Interest = Principal x Rate x Time
where the rate is annual percentage yield (APY) divided by 365 (number of days in a year)
Interest earned in the regular savings account = $1,221.39 x (3.8%/365) x 60 = $17.30
Therefore, the total interest earned between both accounts in 60 days is:
$21.97 + $17.30 = $39.27
So the correct answer is (c) $39.27.
When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.
How should you construct the first statement in a proof?When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.
It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.
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4. The surface area of a cube is 486 in. Find the volume inside the cube but outside of
an inscribed sphere. Round to the nearest tenth.
Answer:
Let s be the length of a side of the cube, then its surface area is given by 6s^2. We know that the surface area of the cube is 486 in^2, so we can set up the equation:
6s^2 = 486
Solving for s, we get:
s^2 = 81
s = 9
Therefore, the length of a side of the cube is 9 in. The radius of the inscribed sphere is half the length of a side, so it is r = 4.5 in. The volume inside the cube but outside of the sphere is equal to the volume of the cube minus the volume of the sphere:
V = s^3 - (4/3)πr^3
V = 9^3 - (4/3)π(4.5)^3
V ≈ 328.8 in^3
Rounding to the nearest tenth, the volume inside the cube but outside of the inscribed sphere is approximately 328.8 in^3.
22. How many positive integers less than 1000 a) are divisible by 7? b) are divisible by 7 but not by 11? c) are divisible by both 7 and 11? d) are divisible by either 7 or 11? e) are divisible by exactly one of 7 and 11? f ) are divisible by neither 7 nor 11? g) have distinct digits? h) have distinct digits and are even?
The set of positive integers less than 1000 that are:
a)Divisible by 7 are 142
b)Divisible by 7 but not by 11 are 130
c)Divisible by both 7 and 11 are 12
d)Divisible by either 7 or 11 are 220
e)Divisible by exactly one of 7 and 11 are 220
f)Divisible by neither 7 nor 11 are 780
g)Having distinct digits are 576
h)Having distinct digits and even are 337
We have,
A whole number that is greater than zero is known as positive integer
a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.
Total terms: 994, divided by 7, plus (n-1)
There are 142 total terms below 1000 that are divisible by 7.
b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.
The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.
c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.
There are 12 total integers below 1000 that can be divided by 77.
d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.
The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.
Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.
e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.
f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.
g)Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),
=> Unique digits from 1 to 100 equal 90.
=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),
=> Unique digits from 101 to 200 are: 100 to 28, 72.
=> Unique numbers between 201 and 1000 = 72 x 8 = 576.
h)Different digits and even values equal to 337
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Please help me !!!!! And show work
Answer:
I have alredy answered this for you. You posted it twice
Step-by-step explanation:
88% of what number is 48
Answer:
54.55
Step-by-step explanation:
can someone please solve #7
The solution to the composite function f(a) + f(h) is f(a) + f(h) = a² - 5a + h² - 5h + 6
Calculating the composite function f(a) + f(h)From the question, we have the following parameters that can be used in our computation:
f(x) = x² - 5x + 3
Using the above as a guide, we have the following:
f(a) = a² - 5a + 3
f(h) = h² - 5h + 3
When these functions are added together, we have
f(a) + f(h) = a² - 5a + 3 + h² - 5h + 3
So, we have
f(a) + f(h) = a² - 5a + h² - 5h + 6
Hence, the solution is f(a) + f(h) = a² - 5a + h² - 5h + 6
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Match the different types of auxiliary views with their descriptions.
used to represent symmetrical objects
only the details of the inclined surface are projected and
drawn in auxiliary view
a single view projected from the primary auxiliary view to
a plane that is inclined to all three principal planes
a single view projected from a secondary or another tertiary
auxiliary view
secondary auxiliary view
half auxiliary view
partial auxiliary view
tertiary auxiliary view
The correct matching is given below:
Used to represent symmetrical objects: Half auxiliary view
Only the details of the inclined surface are projected and drawn in the auxiliary view: Partial auxiliary view
A single view projected from the primary auxiliary view to a plane that is inclined to all three principal planes: Secondary auxiliary view
A single view projected from a secondary or another tertiary auxiliary view: Tertiary auxiliary view
What is the Half Auxiliary View?The half auxiliary view shows one-half of symmetrical objects while partial auxiliary views focus on inclined surface details.
Secondary auxiliary views offer extra angles by projecting from the primary view to an inclined plane. Tertiary auxiliary views expand on this by projecting from secondary/tertiary views to show details. Auxiliary views clarify technical drawings.
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Use the image below to answer the questions. Answers should be fractions in lowest terms.
(a) Find the probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid
(b) Find the probability that a point chosen randomly inside the rectangle and is outside the Triangle
The probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Here, area of a rectangle = Length×Breadth
= 15×8
= 120 square units
Area of a triangle = 1/2 ×Base×Height
= 1/2 ×(√10²-6²)×6
= 0.5×8×6
= 24 square units
Area of a trapezium = 1/2 (Sum of parallel sides)×Height
= 1/2 ×(5+7)×2
= 12 square units
Area of a square = side² = 2²
= 4 square units
(a) Probability of landing in trapezium or Square = 12/120 + 4/120
= 16/120
= 2/15
(b) Probability of landing inside the rectangle but outside the triangle = 16/120
= 2/15
Therefore, the probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.
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Can you please help me solve?
The zeros of the polynomial function are x = -1 and x = 5
Finding the zeros of the polynomial functionFrom the question, we have the following parameters that can be used in our computation:
y = x⁴ - 4x³ - 4x² - 4x - 5
To calculate the zeros of the polynomial function, we create a graph of the polynomial
The point where the graph intersect with the x-axis are the zeros of the polynomial function
using the above as a guide, we have the following:
Zeros: x = -1 and x = 5
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y greater then or less than 8
The equivalent value of the inequality is y > 8 and y < 8
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
A = y greater then or less than 8
On simplifying the equation , we get
y > 8 and y < 8
Hence , the inequality is y > 8 and y < 8
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44 multiplied by 3.5
Answer:
154
Step-by-step explanation:
Because that is right.
Q8
Dave and Sue are community centre workers.
They share the opening of the centre each day.
Their manager shares this work out between Dave and Sue in the ratio 3:1
She makes this rota for the first 16 days of the month.
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Name
Dave
Dave
Dave
Dave
Dave
Dave
Dave
Dave
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
Day 15
Day 16
Name
Dave
Sue
Dave
Dove
The number of open centers dave and sue are 12 and 14
We are given that;
Ratio= 3:1
Number of days= 16
Now,
If the manager shares the work out between Dave and Sue in the ratio 3:1, that means that for every 3 days that Dave opens the center, Sue opens it 1 day. So, a possible rota for the first 16 days of the month could look like this:
Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Name Dave Dave Dave Sue Dave Dave Dave Sue Day 9 Day 10 Day 11 Day 12 Day 13 Day 14 Day 15 Day 16 Name Dave Dave Dave Sue Dave Dave Dave Sue
Therefore, by the given ratio the answer will be 12 and 14.
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please help will mark brainliest !!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Divide √9x² by √18y²
When the expression √9x² is divided by √18y², we get result which is equal to x/2y.
To simplify the expression √9x²/√18y², we need to first simplify the square roots in the numerator and denominator.
√9x² = √(3²)(x²) = 3x
√18y² = √(2²)(3²)(y²) = 2(3y)
So, √9x²/√18y² can be written as:
(3x)/(2(3y))
We can simplify this expression by canceling out the common factor of 3 in the numerator and denominator:
(3x)/(2(3y)) = (x)/(2y)
Therefore, the simplified expression of √9x²/√18y² is x/2y.
In conclusion, the expression √9x²/√18y² can be simplified to x/2y by factoring out the common factors from the numerator and denominator, and then canceling out the common factor of 3.
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The area of triangle G is 8 square centimeters. What is the Area of triangle H?
Answer:
The answer is 32cm²
Step-by-step explanation:
Area of triangle G=8cm²
A=1/2×xy=8cm²
Area of triangle H=?
A=1/2×4x×4y
A=4×area of triangle G
A=8×4=32cm²
Linda is discussing her interior design ideas for a children’s playroom with her client. What type of drawing will be useful to express her ideas to her client?
Linda can represent the different kinds of spaces she has planned for the playroom through a _________ diagram.
Answer:
A floor plan diagram would be useful for Linda to express her ideas to her client.
In a right triangle, one leg measures 4 inches and the other leg measures 6 inches. What is the length of the hypotenuse in inches.
The length of the hypotenuse in this right triangle is 2√(13) inches.
Now, in the given right triangle, we are given the lengths of the two legs, one measures 4 inches and the other measures 6 inches. We need to find the length of the hypotenuse. To do that, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In other words, if we let a and b be the lengths of the legs, and c be the length of the hypotenuse, then:
c² = a² + b²
In this case, we have a = 4 and b = 6. So, we can plug these values into the formula and solve for c:
c² = 4² + 6² c² = 16 + 36 c² = 52
To find c, we take the square root of both sides:
c = √(52)
We can simplify this by factoring 52 into its prime factors: 52 = 2² x 13. Then we can take the square root of each factor:
c = √(2² x 13) c = 2√(13)
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Solve the equation e' = 120. Then find the approximate value of the solution
using a calculator.
The approximate value of the solution to the equation e' = 120 is e ≈ 120.the value of e by rounding it to a Reasonable number of Decimal places.
The given equation is e' = 120, where e represents some variable.
To solve for e, we can start by dividing both sides of the equation by the coefficient of e, which is 1:
e' / 1 = 120 / 1
Simplifying the right-hand side, we get:
e' = 120
This means that the value of e is equal to 120. So the solution to the equation e' = 120 is e = 120.
To find the approximate value of e, we can use a calculator to evaluate the expression. Since e is a variable, we cannot substitute it directly into the calculator. However, we can estimate the value of e by rounding it to a reasonable number of decimal places.
In this case, since e' is given as 120, we can assume that e is also in the same units. So we can round e to the nearest whole number:
e ≈ 120
Therefore, the approximate value of the solution to the equation e' = 120 is e ≈ 120.
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which range contains the value of √4(4+3)
a: between 2.6 and 2.7
b: between 4.3 and 4.5
c: between 5.2 and 5.4
d: between 7.4 and 7.6
[tex]\sqrt{4(4+3)}[/tex] is between 5.2 and 5.4.
Answer:
Step-by-step explanation:
Here first look at the quantity which is [tex]4(4+3)=16+12=28[/tex]. So the nearby largest possible of square root which gives us integer is 25. So [tex]5=\sqrt{25} < \sqrt{28}[/tex] is satisfied.
So now looking at the options we can say that [tex]5.2^{2}=27.04[/tex] and [tex]5.4^{2}=29.16[/tex]. We can see that [tex]27.04 < 28 < 29.04[/tex].
Final Answer: So the answer is b)between 5.2 and 5.4.
the question is attached
The exponential equations in the question indicates that solution for the equation are;
The solution to the system of equations y = f(x) and g(x) are (0, 7), and (2, 4). The solution of the system of equation f(x) = g(x) are 0 and 2
What is a system of equation?A system of equation is a set of equations that share the same variables.
The solution of the graphical equations are the points where the graph intersects the x-axis.
The solution are therefore; y = f(x) = 0 = 4(2)⁻ˣ + 3
4(2)⁻ˣ = -3
(2)⁻ˣ = -3/4
-x·ln(2) = ln(-3/4)
x = -ln(-3/4)/ln(2) (No real solution)
However, the solution of the system of equation is the points where the graphs of the equations intersect. The graph indicates that the solution points are (0, 7), and (2, 4)
Therefore, the x-values of the solution are; x = 0, and x = 2
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StartFraction 27 Over 9 EndFraction = StartFraction 18 Over x EndFraction a. x = 9 c. x = 6 b. x = 18 d. x = 3
The value of the fraction is x = 6 (option c).
In this problem, we are given an equation involving fractions:
27/9 = 18/x
To solve this equation, we can start by simplifying each fraction. Both 27 and 9 are divisible by 9, so we can simplify the left-hand fraction as follows:
3/1 = 18/x
Similarly, we can simplify the right-hand fraction by dividing both the numerator and denominator by 18:
3x = 18
x = 18/3 = 6
Therefore, the answer to this problem is option c. x = 6.
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The triangle above has the following measures.
s = 29 m
r= 63 m
Find the m/Q.
Round to the nearest tenth and include correct units.
Show all your work.
The value of m∠Q as shown in the right-angled triangle below is 62.59°.
The Formula used is:
m∠Q = cos⁻¹(s/r)........................ (1)
Where:
s = 29 m
r = 63 m
Now, Substitute these values into equation 1
m∠Q = cos⁻¹(29/63)
m∠Q = cos⁻¹(0.46)
m∠Q = 62.59°
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The coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)
The perimeter and area of the square are; 24√2 units and 12 units² respectively
Given the coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)
But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.
SQ = √(x₂ - x₁)² + (y₂ - y₁)²
SQ = √(2 - (-4)² + (5 - 11)²
SQ = 6√2
Let's find QU
QU = √(-4 - 2)² + (-1 - 5)²
QU = 6√2
Let's find UA ;
UA = √(-10 - (-4))² - (5 - (-1)²
UA = 6√2
And the distance AS = 6√2
The perimeter of the square = 4 (6√2)
Perimeter = 24√2 units
The area of the square = l²
Area of the square = (6√2)²
Area of square = 12 units²
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WEATHER Paola’s weather app tells her that there is a 20% chance of rain on Tuesday and a 50% chance of rain on Wednesday. What is the probability that it will rain on both Tuesday and Wednesday?
The probability that it will rain on both Tuesday and Wednesday is 60%.
Let A represents the event of raining on Wednesday and B represents the event of raining in Tuesday,
Then according to the question,
P(A) = 20% = 0.2,
P(B) = 50% = 0.4,
Here, A and B are independent events,
So, P(AB) = P(A) × P(B),
⇒ P(A∩B) = 0.2 × 0.5 = 0.10
We know that,
P(A∪B) = P(A) + P(B)
The probability it rains on Wednesday or Tuesday, P(A∪B) = 0.2 + 0.5 - 0.10
= 0.60
= 60%
Hence the probability that it will rain on both Tuesday and Wednesday is 60%.
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In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 5 inches. What percentage of the students are taller than 72 inches tall, to the nearest tenth
The probability is 0.160, that a randomly selected student will be taller than 72 inches.
We have,
'Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.'
mean (μ) = 68 inches
Standard Deviation (σ) = 3
We know,
Z = mean/ standard deviation
From the normal distribution bell curve, we can see that the percentage of students taller than 72 inches = 14% + 2%
= 16%
The probability that a randomly selected student will be taller than 72 inches = 16/100
= 4/25
= 0.16
= 16%
Hence, we can conclude, that the probability that a randomly selected student will be taller than 72 inches is 0.160
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