Answers
The expression [tex](\frac{1}{4^{-3 } } )^{-2}[/tex] is less than 1.
The sign to change to make the expression greater than 1 is changing the sign of the exponential value which will make the new expression as
[tex](\frac{1}{4^{-3 } } )^{2}[/tex]
What is expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).
In other words, an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.)
Therefore, let's simplify the expression to know if it's equals to 1, greater than 1 or less than 1.
[tex](\frac{1}{4^{-3 } } )^{-2}[/tex]
using law of indices,
[tex](\frac{1}{4^{-3 } } )^{-2}[/tex] = 1 × [tex](4^{-3} )^{2}[/tex]
4⁻⁶ = 1 / 4⁶ = 1 / 4096
Hence,
1 / 4096 = 0.00024414062
Therefore, the value is less than 1.
Let's change one sign to make the expression greater than 1.
Therefore, the expression will be [tex](\frac{1}{4^{-3 } } )^{2}[/tex]
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Related Questions
Evaluate the exponential functions
Answers
I hope this helps. Have a great rest of your day!
Oliver saves 10% of his weekly earnings for living expenses. He usually makes $520 each week. This week he made 10% more. Oliver incorrectly claims that he has $520 left for spending money this week.
Answers
Answer:
10% of $520
=$52
Money made this week :
$520+$52=$572
Saving:
10% of $572
=$57.2
Money left:
$572-$57.2=$514.8
Please mark as brainliest
Answer: We have been given that,
Oliver's weekly earnings = $520
His earnings this week = 10% of $520 +$520
= $520+$52= $572
As he saves 10% of his weekly earnings so he would have been left with
= 10% of $572
= $57.2
So, he only has $52.7 left for spending money this week
Step-by-step explanation:
Which of the quotients is equivalent to -5/8? Select all that apply.
Answers
The equivalent quotient to -5/8 are; -5/8 and .5/-8.
The correct answer options are options A and C
How to find equivalent quotient?A quotient is the number resulting from the division of one number by another. For instance, the quotient of 12 divided by 4 is 3.
A divisor number or expression that another is to be divided by. For instance, in "42 ÷ 3" the divisor is the 3.
Dividend is a number or expression that is to be divided by another. For instance, In "42 ÷ 3" the dividend is the 42.
Complete question:
Given options:
A. -5/8
True
B. 5/8
False
C.5/-8
True
D. -(5/-8)
False
E. -5/-8
False
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Find the circumference and the area of a circle with diameter 7 cm.
Answers
The circumference of the circle is 21.98cm and the area of the circle is 38.465 square cm.
Circumference of the circle:
The Circumference (also known as) perimeter of circle = 2πR
where,
R is the radius of the circle
π is the mathematical constant with an approximate value is 3.14.
Area of circle:
The formula to find the area of the circle is;
A = πr²
Where r represents the radius of the circle.
Given,
The diameter of the circle is 7 cm.
Here we need to find the circumference and the area of a circle.
Here we have the value of diameter, in order to find the circumference we have to find the value of radius that can be derived by dividing the diameter by 2.
So, the radius is
=> 7/2 = 3.5
Now the circumference of the circle is calculated as,
C = 2 x π x 3.5
When the value of π = 3.14
Therefore, the circumference of the given circle is,
=> C = 2 x 3.14 x 3.5
=> C = 21.98
Now, the area of the circle is,
=> A = π x (3.5)²
=> A = 3.14 x 12.25
=> 38.465
Therefore, the area of the circle is 38.465 square cm.
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Factor of 14a–35? Pls Ty
Answers
what did i do wrong? how do i do y-int?
Answers
What is the first step to find the quotient of a long division problem?
Divide the terms with the highest degree
Multiply terms by the divisor
Subtract the product from the dividend
Place the result in the quotient
Answers
The first step to find the quotient of a long division problem is to Divide the terms with highest degreee
What is quotient of a long division?A quotient is a quantity produced by the division of two numbers. For example 16/4 ,the number that is being divided (in this case, 16) is called the dividend, and the number that it is being divided by (in this case, 4) is called the divisor. The result of the division(5) is the quotient.
The step that is needed to find a quotient of a division are
1.Divide the terms with the highest degree
2.Multiply terms by the divisor
3.Place the result in the quotient
4. Subtract the product from the dividend
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4. Enrique collected 152 recyclable bottles, and
Latasha collected brecyclable bottles. Write
an expression for the number of bottles they
collected altogether.
Answers
The required expression is Total = 152+x .
What is expression ?
Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
Here,
The number of bottles Enrique collected = 152
Let us take number of bottles collected by Latasha as x. Then,
Total number of bottles collected by the is ,
=> Total = Number of bottles collected + Number of bottle collected
by Enrique By Latasha.
=> Total = 152+x
Hence the required expression is Total = 152+x.
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Critical thinking questions:
Write a system of equations with the solution (4, -3).
Answers
Answer: (4,-3)
Step-by-step explanation:
4x+5y=1 (1)
3x-2y=18 (2)
Multiply both parts of equation (1) by 2 and both parts of equation (2) by 5:
8x+10y=2
15x-10y=90
Sum these equations:
23x=92
Divide both parts of the equation by 23:
x=4
Substitute the value of x=4 into equation (1):
4(4)+5y=1
16+5y=1
16+5y-16=1-16
5y=-15
Divide both parts of the equation by 5:
y=-3
Thus, (4,-3)
What is the reason for each step in the solution of the equation?
−6x=−2(x+12)
Drag and drop the reasons into the boxes to correctly complete the table.
Answers
Answer:
Given
Distributive Property
Addition Property of Equality
Division Property of Equality
Step-by-step explanation:
Frist you distribute the -2 by multiplying it to everything in the parentheses. Next, you add 2x to both sides of the equation and lastly you divide both sides of the equation by -4
The money used in Switzerland is called
the Franc. The exchange rate is $5 for 6
Francs. Find how many dollars you would
receive if you exchanged 18 Francs.
Answers
put them in form of fractions where
$5/6 francs = x(unknown $)/18 francs
then cross multiply numbers
6 times x = 6x
5(18)=90
divde both by 6
90/6=15
6x/6=x
x=15
furthermore to prove it 15/18 can be reduced to 5/6
What is the sale price including tax to the nearest cent? $595 refrigerator, 20% discount; 9.25% tax
Answers
The sale price including tax for the refrigerator is $520.
How to calculate the price?From the information, the following can be deduced:
Refrigerator = $595
Discount = 20%
Tax = 9.25%
The sales price will be:
= Refrigerator price + Tax - Discount
= $595 + (9.25% × $595) - (20% × 650)
= $595 + $55 - $130
= $520
The price is $520.
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A submarine was 400 meters below sea level it then moved to 583 meters below sea level. How many meters did the submarine descend? how did you get the answer?
Answers
Answer:
Step-by-step explanation:
You subtract 583 from 400 (400-583)
Then you get 183
winner gets brainiest | Don't type in any bs Actually answer the question please
Find domain and range of this linear graph
Answers
Answer:
Domain: {0 \leq x} Range {0 \leq y}
Step-by-step explanation:
btw \leq means less than or equal to
(6, y) and (-8, 4); slope: 1/7
Answers
For the given points (6, y) and (-8, 4) having slope = 1/7 the value of y = 10.
What is the slope of a line?
A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.
If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula
[tex]Slope(m)=\frac{d - b}{ c - a}[/tex]
The given points are (6, y) and (-8, 4).
and the slope of the line is given as m = 7.
By using the slope of a line formula, we get
[tex]m = \frac{8-y}{-8-7}\\\\ \frac{1}{7}= \frac{8-y}{-8-7}\\\\\frac{1}{7}= \frac{8-y}{-14}\\\\\\8-y=-2\\y=8+2\\y=10[/tex]
Hence, the value of y is 10.
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48 - (3 c+4)=4(c+5)+3 c=???
Answers
Answer in multiple forms depending on what needed
Answer:
c = 3
Step-by-step explanation:
48- (3c+4)=4(c+5)+3
48-3c-4=4(c+5)+3 Distributed the - sign
48 -3c -4= 4c+20 +3 Distributed the 4
44-3c =4c+23 Combined like terms
21-3c=4c Subtract 23 from both sides
21=7c Add 3c to both sides
3=c
Hello, please answer this correctly and you will get 5 stars and 20 points.
Answers
Answer:
Step-by-step explanation:
90
A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is 24-ft by 26-ft rectangle, and the pavers measure 6 inches across the flats, how many pavers are needed?To surface a driveway about _ pavers are needed
Answers
The number of pavers required is 961.
The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.
Given data
A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is a 24-by-26-foot rectangle with pavers 6 inches wide across the flats.
We have to determine how many pavers are needed
We know that area of a regular hexagon
A = (3√3)/2 a^2
= (3√3)/2 〖(6)〗^2
= (3 x 1.732)/2 x 36
= 93.528 sq.inches
Now area of rectangle
= l x w
= 24 x 26 x (12)2 (1feet = 12 inches)
= 89856 sq.inches
Now pavers required
= 89856/93.528
= 960.73
= 961
Therefore the number of pavers required is 961.
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The equation of line p is y + 5 = -10(x + 2). Line q is perpendicular to line p and passes
through (-1, -1). What is the equation of line q?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
ojo
Submit
Work it out
Not feeling ready vet? These can help:
Ver en
Answers
The equation of line q is y = x/10 - 9/10.
What is equation of straight line?
A line that does not curl or bend is said to be straight. A line has length but no width, making it a one-dimensional figure. A line consists of points that extend infinitely in opposite directions. Two points in a 2D plane determine it. A, B, and C are real-based constants in the formula Ax + By + C = 0, A, B 0. The geometric representation of the equation is always a straight line.
Here the given line P,
=> y+5=-10(x+2)
=> y+5=-10x-20
=> y = -10x-25
Here in the given line y=mx+c , where m=slope. Then,
=> Slope of line P = -10.
Here line P is perpendicular to line q.
Then, slope of line q = -1/ slope of line p = -1/-10 = 1/10
Now the line passes through the point [tex](x_1,y_1)=(-1,-1)[/tex] then,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y+1 = 1/10 (x+1)
=> 10y+10 = x+1
=> 10y=x-9
=> y = x/10 - 9/10.
Hence the equation of the line q is y = x/10 - 9/10.
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I NEED HEEEEELP!!
There are 5 cockroaches crawling on each square meter of the front of this building. How many cockroaches are crawling on the front of the building?
Please, show your work and explain. TYSM!! ^^
Answers
There are 855 cockroaches crawling on the front of the building
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
The population density is given as:
Population density = total animals / area occupied
Given that, the population density of the cockroaches is 5 cockroaches per square meter.
The area of the building = area of triangle + area of square
Area of building = (1/2) * (24 - 9)(12) + (9 * 9) = 90 + 81 = 171 m²
Population density = total animals / area occupied
5 cockroaches per square meter = Total cockroaches / 171 m²
Total cockroaches = 855
There are 855 cockroaches
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Question 2b answer please
and working out
Answers
Answer:
20 mph
Step-by-step explanation:
If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph
50. WATER HOSES A water hose can spray water at an
initial velocity of 40 feet per second. Use the formula
h(t) = vot – 16t², where h(t) is the height of the water
in feet, vo is the initial velocity in feet per second, and
t is the time in seconds.
-
a. How long will it take the water to hit the
nozzle on the way down?
b. Assuming the nozzle is 5 feet up, what is
the maximum height of the water?
Answers
It will take 2.5 seconds for the water to hit the nozzle on the way down if the initial velocity is 40 feet per second. The maximum height of the water is 30 feet if the nozzle is 5 feet up.
a) Given equation
h(t) = v₀t - 16t^2
Substitute v₀ = 40, h(t) = 0 in the given equation
40t - 16t^2 = 0
Solve for t
⇒ 16t^2 = 40t
⇒ 16t = 40
⇒ t = 40/16
⇒ t = 2.5 seconds
Hence, water will take 2.5 seconds to hit the nozzle on the way down.
b) The function that represents the given condition
h(t) = -16t^2 + 40t + 5
The maximum value of the function is the y-coordinate of the vertex.
The x-coordinate of the vertex
= -40/2(-16) = 5/4
Find the y-coordinate of the vertex by substituting t = 5/4
⇒ h(5/4) = -16(5/4)^2 + 40(5/4) + 5
⇒ h(5/4) = -25 + 50 + 5
⇒ h(5/4) = 30
Hence, the maximum height of the water is 30 ft.
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Colton made a scale drawing of a city park. In real life, the soccer field is 90 meters long.
It is 18 millimeters long in the drawing. What scale did Colton use?
Answers
By using unitary method it is obtained that -
Scale used my Colton = 1 : 500
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here unitary method is used
18 mm long field in the drawing is equivalent to 9000 mm long field in real
1 mm long field in the drawing is equivalent to [tex]\frac{9000}{18}[/tex] mm long field in real
1 mm long field in the drawing is equivalent to 500 mm long field in real
Scale used by Colton 1 : 500
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According to the graph provided, the weight for someone who is 1.4 meters tall is predicted to be close to kilograms
Answers
According to the scatterplot (graph) provided, the weight for someone who is 1.4 meters tall is predicted to be 34.8 kilograms.
What is a scatterplot?A scatterplot is also referred to as scatter diagram, scattergram, or scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association between the data set.
For this exercise, the height (M) was plotted on the x-axis of the scatterplot (graph) while the weight (in kg) would be plotted on the y-axis of the scatterplot (graph).
From the scatterplot which models the relationship between the height (M) and weight (in kg) of a person, an equation for the line of best fit is given by:
Weight, kg = -114.3 + 106.5M
When M = 1.4 meters, we have the following weight:
Weight, kg = -114.3 + 106.5(1.4)
Weight, kg = -114.3 + 149.1
Weight, kg = 34.8 kg.
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Complete Question:
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be close to ____ kilograms.
The second and fifth terms of a geometric sequence are 750 and -6 respectively. Find the
common ratio and first term of the sequence.
Answers
Step-by-step explanation:
T2= -6
T5=750
ar=-6
ar4=750
both a's cancel each other
we have;
r=-6
r4=750
r4-1(The law of indices) =750
r3=750
r=3√750
r=9.1
The number of computer security breaches is expected to increase at a yearly rate of 86%
Use the exponential growth model to determine the equivalent monthly rate.
Enter the rate, to the nearest tenth of a percent, in the box.
____%
Answers
Answer:
The population is expected to grow at a rate of 1.36% each year. What is the population of the town in 2006? Round your answer to the nearest whole number.
Step-by-step explanation:
Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
Answers
The values of x and y are 2 and -7 respectively, this forms an ordered pair of (6,-7) and (2,1).
What are the the values of x and y to complete the given ordered pair?Given the equation and ordered pair the question;
y = -2x + 5Point: (6,y) Point; (x,1)To determine, the y-value, plug the x-value into the equation and solve for y.
y = -2x + 5
Plug in x = 6
y = -2( 6 ) + 5
y = -12 + 5
y = -7
Determine the x-value by plunging in the y-value into the equation and solve for x.
y = -2x + 5
Plug in y = 1
1 = -2x + 5
1 + 2x = 5
2x = 5 - 1
2x = 4
x = 4/2
x = 2.
Therefore, the ordered pair are (6,-7) and (2,1).
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At Happy Tails Animal Boarding, cat food and dog food is purchased weekly, Last week, Karen purchased 6 bags of cat food and 9 bags of dog food for a total of 117$. This week, she purchased 4 bags of cat food and 7 bags of dog food for a total of 87$.
Assuming the prices for cat and dog food have not changed over the past two weeks, find and solve the system of equations which can be used to determine the cost of a bag of cat food, c, and the cost of a bag of dog food, d.
c=cost of a bag of cat food
d=cost of a bag of dog food
Write Two Equation
?
?
Answers
One bag of cat food costs $6 and one bag of dog food costs $9.
What is system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
The problem states that c equals the cost of bag of cat food and d equals the cost of bag of dog food.
Last week she paid $117 for 6 bags of cat food and 9 bags of dog food.
Therefore, the equation becomes,
6c + 9d = 117 ..(1)
This week she paid $87 for 4 bags of cat food and 7 bags of dog food.
Therefore, the equation becomes,
4c + 7d = 87 ..(2)
Now to solve the system of equations
To solve the first equation for c.
6c + 9d = 117
6c = 117 - 9d
[tex]c = \frac{117}{6}-\frac{9d}{6}[/tex]
Plug value of c in equation (2).
[tex]4(\frac{117}{6}-\frac{9d}{6}) +7d = 87\\78 - 6d + 7d = 87\\d = 87-78\\d = 9[/tex]
Plug d = 9 in equation (1)
6c + 9(d) = 117
6c + 9(9) = 117
6c + 81 = 117
6c = 117 - 81
6c = 36
c = 6
Hence, one bag of cat food costs $6 and one bag of dog food costs $9.
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The laundry room at a hotel sent 160 bath
towels and 64 washcloths to the most rooms
they could so that each room received the
same number of each type of towel. How
many bath towels and how many washcloths
went to each room?
Answers
Answer:
5 bath towels
2 washcloths
Step-by-step explanation:
160 = 2⁵ × 5
64 = 2⁶
HCF= 2⁵ = 32
160 ÷ 32 = 5
64 ÷ 32 = 2
What is the first step needed to solve 4 over 7 multiplied by x minus 5 equals negative 13 ? (1 point)
Group of answer choices
Add 5 to both sides
Multiply both sides by 4
Subtract 13 from both sides
Divide both sides by 7
Answers
Answer:add 5 to both sides
Step-by-step explanation:
