Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]4-\frac{11}{3}=\frac{4*3}{1*3}-\frac{11}{3}\\\\=\frac{12}{3}-\frac{11}{3}\\\\=\frac{12-11}{3}\\\\=\frac{1}{3}\\\\\\4-\frac{2}{3}=\frac{4*3}{1*3}-\frac{2}{3}\\\\=\frac{12}{3}-\frac{2}{3}\\\\=\frac{12-2}{3}\\\\=\frac{10}{3}[/tex]
[4 - 11/3] ÷ (4 - 2/3) = [1/3] ÷ (10/3)
[tex]=\frac{1}{3}*\frac{3}{10}\\\\=\frac{1}{10}[/tex]
Use the graph of f to describe the transformation that results in the graph of g. f(x) = log x; g(x) =
Answer:
The function was expanded vertically by 5, and then translated vertically upwards 6 units.
Which is the third option in the list of possible answers.
Step-by-step explanation:
Recall that the types of transformations associated with:
A) a function multiplied by a positive factor larger than one consists on the function expanded vertically by that factor.;
B) a positive number added to the function consists on the vertical translation of the function upwards as many units as the number added.
Therefore, the function [tex]f(x) = log(x)[/tex] being transformed into [tex]g(x)=5\,log(x)+6[/tex]
consists of the initial function expanded vertically by 5, and then translated vertically upwards 6 units.
Can someone help me out please :)
Students in a class sit two major exams.
75% of students pass the maths exam.
80% of those who pass
the maths exam
also pass the science exam. 40% of those
who fail the maths exam pass the science
exam. Find the probability that a student
chosen at random:
(b) fails both exams.
%
Answer:
15%
Step-by-step explanation:
25% fail math
60% of the 25% above fail science
thus,
[tex] \frac{25}{100} \times 60\%[/tex]
=15% of total student
What shape will you get if you take a cross section of a square pyramid parallel to its base? ANSWERS: A rectangle A triangle A square A parallelogram
Answer:
A square
Step-by-step explanation:
Since the base is a square, any plane of the pyramid parallel to the base is shaped like a square (except the very top one which is a point).
Square shape will you get if you take a cross section of a square pyramid parallel to its base
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
'A square pyramid is a three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.'
According to the given problem,
If a square pyramid is cut along the plane, then the cross-section of the solid is square. Because it is a square pyramid.
Hence, we concluded that square could be formed by slicing the square pyramid by a plane.
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Graph the linear equation,find three points that solve the equation,then plot on the graph. -4y=x-18
Answer:
Step-by-step explanation:
The equation given to us is:
-4y = x-18
y = (x-18)/-4
Substitute x = 0:
y = (0-18)/-4
y = 4.5
Substitute x = 18
y = (18-18)/-4
y = 0
Substitute x= -18
y = (-18-18)/-4
y = -36/-4
y = 9
The three points found are (0,4.5), (18,0), (-18,9)
Graph all three point onto the coordinate plane.
Join all three point with a line, and extend the line.
The line shows the graph for -4y=x-18
Answer:
(-6,3) (-2,4) (2,5)
Step-by-step explanation:
A store manager asks every 25th person to enter the store which sales they like the best. Which type of data collection method is described in this situation?
A.observational study
B. experiment
C. sample survey
D. None of the choices are correct.
The correct answer is C. Sample survey
Explanation:
A sample survey is a study method that involves selecting a portion of a population and asking questions to these individuals to know their opinions or insights about a particular situation. Additionally, the answers provided by the selected individuals are used to make conclusions about all the population. This method is the one used in the situation described because the store manager selects only some customers to know about the sales they prefer and would likely use this information to know the preferences of all the customers.
This year at the state fair they held two hot dog eating contests. The first contest had 19 contestants and the winner would be the person that ate the most regular-sized hot dogs in 15 minutes. The second contest had 23 contestants and the winner would be the person that ate the most jumbo-sized hot dogs in 15 minutes. The data from both contests are shown in the box-and-whisker plots above. Using the box-and-whisker plots, the results for the____-sized hot dog contest has greater variability. The difference in the medians of the two contests is approximately _____times the interquartile range.
Answer:
*regular-sized hot dog contest has greater variability
*The difference in the medians of the two contests is approximately 2 times the interquartile range.
Step-by-step explanation:
Variability of the data from both contests can be compared using the range or interquartile range of each set of data from both contests.
The greater the value of the range or interquartile range, the greater the variability.
Range for regular-sized hot dog contest = 32 - 17 = 15
Range for Jumbo-sized hot dog contest = 22 - 8 = 14
Interquartile range for regular-sized hot dog contest = 27 - 22 = 5
Interquartile range for jumbo-sized hot dog contest = 16 - 11 = 5
Median for regular-sized hot dog contest = 23
Median for jumbo-sized hot dog contest = 14
The difference in the median of both contests = 23 - 14 = 9, which is approximately 2 times the interquartile range (5)
Thus, results for the regular-sized hot dog contest has greater variability, be side its range is 5, which is greater than that for jumbo-sized contest.
The difference in the medians of the two contests is approximately 2 times the interquartile range.
The interquartile range of both contests is 5. The median difference between both contests is 9, it is approximately 2 times 5. (i.e. 9/5 = 1.8 ≈ 2).
9 cans of paint are needed to
paint 4 rooms. Exactly how
many cans of paint are needed to
paint 10 rooms? How many cans
of paint should be purchased?
Exact:
Purchased:
Answer:
Step-by-step explanation:
Write and solve an equation of ratios:
9 4
----- = -----
x 10
Then 4x = 90, and x = 22.5
It will take exactly 22.5 cans of paint to cover 10 rooms. The painter must buy 23 cans.
Jason can mow his parents' yard in 3 hr. His brother can mow it
in 4 hr. How long would it take them, working together, to mow
the yard? (Assume two mowers are available.)
I would assume it would take 3.5 hours to mow the lawn together.
Help please. (Given: y ∥ x Prove: m∠5 + m∠2 + m∠6 = 180)
Answer:
Step-by-step explanation:
Concepts used :
sum of angles at a point on straight line is 180
if a transversal intersects two parallel lines then alternate angles are equal.
____________________________________________
∠∠∠∠∠
m∠1 + m∠2 + m∠3 = 180 ____________(A)
reason :sum of angles at a point on straight line is 180
these angles lie on LAM at point A
m∠1 = m∠5
Reason: alternate angles y ∥ x and AC is transversal
m∠3 = m∠6
Reason: alternate angles y ∥ x and AB is transversal
Substituting m∠1 with m∠5 and m∠3 with m∠6
in equation A---m∠1 + m∠2 + m∠3 = 180
m∠5 + m∠2 + m∠6 = 180
Hence proved.
Answer:
The answers are below. Hope this helped. I sacrificed my answers ˙-˙ :)
Step-by-step explanation:
<1 congruent to <5 Given
<3 congruent to <6 Alternate Interior Angles theorem
m<1 = m<5 Alternate Interior Angles theorem
m<3 = m<6 Definition of congruent angles
m<1+m<2+m<3=m< LAM Definition of congruent angles
m<1+m<2+m<3=180 Angle additon postulate
m<5+m<2+m<6=180 Definition of straight angle
The diagram shows a solid shape.
The volume of the cone is 270 cm.
Work out the volume of the solid shape.
Give your answer in terms of pi
Answer:
[tex]756\pi[/tex]
Solution,
Volume of cone=270 pi cm^3
[tex] \frac{1}{3} \pi \: {r}^{2} = 270\pi \\ or \: {r}^{2} \times 10 = 270 \times 3 \\ or \: {r}^{2} \times 10 = 810 \\ or \: {r}^{2} = \frac{810}{10} \\ or \: {r}^{2} = 81 \\ or \: r = \sqrt{81} \\ or \: r = \sqrt{ {9}^{2} } \\ r = 9 \: cm[/tex]
Volume of semisphere:
[tex] \frac{2}{3} \pi {r}^{3} \\ = \: \frac{2}{3} \times \pi \times 9 \times 9 \times 9 \\ = 486\pi[/tex]
Total:
[tex]270\pi + 486\pi \\ = 756\pi[/tex]
hope this helps...
Good luck on your assignment..
a squared paper shows the nets of cuboid A and cuboid B. do the two cuboids have the same surface area? plzzzzzzzzz answer
Answer:
No it doesn't have the same surfaces
The cuboid A and B have different surface areas.
What is surface area?The surface area of a three-dimensional object is the total area of all its faces.
Formula for the surface area of cuboidSA=2lw + 2lh + 2hw
Where,
SA is the surface area of a cuboid
l is the length of the cuboid
h is the height of the cuboid
w is the width of the cuboid
Let the area of each cube is one unit.
So, for the cuboid A
Length = 3 unit
Width = 2 unit
Height = 3 unit
Therefore, the surface area of cuboid A = ( 3 × 2 + 3 × 2 + 2 × 2 ) 2
⇒ Surface area of cuboid A = 32 square unit
For cuboid B
Length = 4 unit
Width = 1 unit
Height = 3 unit
Therefore,
The surface area of cuboid B = (4 × 1 + 4 × 3 + 3 × 1)2
⇒ Surface area of cuboid B = 38 square unit
Hence, the cuboid A and B have different surface areas.
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solve the math problem please
Answer:
B, x≥2
Step-by-step explanation:
54 - 10x ≤ 20 + 7x - subtract 20
34 - 10x ≤ 7x - add 10x to 7x
34 ≤ 17x - divide 34 by 7
2 ≤ x - flip the equation - x ≥ 2
Hope this is helpful!
Answer:
Choice B
Step-by-step explanation:
TRUST ME. IF YOU WANT EXPLANATION:
54 - 10x < = 20 + 7x
54 - 20 < = 7x + 10x
34 < = 17x
34/17 < = x
2 < = x.....or x > = 2....its B trust me
a particular strain of bacteria doubles in population every 10 minutes. Assuming you start with a single bacterium in a petri dish, how many bacteria will there be in 2.5 hours? A. 16,384 B. 65,536 C. 32,768 D. 9536
Answer:
C. 32,768
Step-by-step explanation:
Step 1
Convert the number of hours to minutes
2.5 hours to minutes = 2 hrs 30 minutes to minutes is calculated as
1 hour = 60 minutes
2 hours 30 minutes =
Cross multiply
(60 minutes × 2 hours) + 30 minutes = 150 minutes.
Step 2
We are told in the question that the bacteria population doubles every 10 minute interval
Find the number of intervals in 150 minutes
= 150 minutes / 10 minutes interval
= 15 intervals
Step 3
The number of bacteria present after 2.5 hours is calculated using the formula of
= Amount of bacterium × 2ⁿ
Where n = number of intervals = 15
Amount of bacterium = single bacterium = 1
Number of bacteria = 1 × 2¹⁵
= 32,768
Therefore, when you start with a single bacterium in a petri dish, the number of bacteria that will there be in 2.5 hours is 32,768
what is the recursive formula for this geometric sequence? 2,-10,50,-250,...
Answer:
an = an-1 * (-5)
a1= 2
Step-by-step explanation:
The recursive formula is
an = an-1 * r
a1= initial term
where a1 is the initial term and r is the common ratio
a1 =2 or the starting term
r = second term / first term = -10/2 = -5
an = an-1 * (-5)
a1= 2
Answer:
The correct answer is D
Step-by-step explanation:
2 and -5
Thuy rolls a number cube 7 times. Which expression represents the probability of rolling a 4 exactly 2 times? P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction Subscript 7 Baseline C Subscript 5 Baseline (one-sixth) squared (one-sixth) Superscript 5 Subscript 7 Baseline C Subscript 5 Baseline (one-sixth) Superscript 5 Baseline (five-sixths) squared Subscript 7 Baseline C Subscript 2 Baseline (one-sixth) squared (five-eighths) Superscript 5 Subscript 7 Baseline C Subscript 2 Baseline (two-sixths) squared (four-sixths) Superscript 5
Answer:
Rolling a 4 on the first try has a probability of (1/6). Meaning, it is one event out of the six possible events of the die. Rolling a 4 a second time also has a probability of (1/6), because nothing has changed on the die.
Answer:
Subscript 7 Baseline C Subscript 2 Baseline (one-sixth) squared (five-eighths) Superscript 5
Step-by-step explanation:
The answer above is correct.
PLEASE HELP
Prison M and pyramid N and have the same base area and the same height. Cylinder P and prism Q have the same height in the same base perimeter. Come Z has the same base area of cylinder y, but its height is three times the height of the cylinder y. The figures? And? Have the same volume
9514 1404 393
Answer:
Cone Z, cylinder Y
Step-by-step explanation:
Pointy objects such as pyramids and cones have 1/3 the volume of a prism (or cylinder) with the same base area. So, for a cone and cylinder of the same base area to have the same volume, the cone must be 3 times as high.
The figures described as having that relationship are ...
cone Z, cylinder Y
_____
Additional comment
The perimeter of a prism is not sufficient to define its base area, unless the shape of the base is well-enough defined. However, the perimeter of the base is useful for determining the lateral surface area. Unfortunately, that is not of any interest in this problem.
PLEASE HELP!!!!
Find the product. Write your answer in
exponential form.
2^6•2^-5
Answer:
2^1
According to the product of powers with the same base, a^m * a^n = a^m+n.
Basically, when you're multiplying exponents with the same base, you can add the powers together to get the answer.
2^6 * 2^-5
The bases are the same, so we can apply this rule.
6 + -5 = 1
This gives you the answer of 2^1.
9/7 times (-9/5) please help
Answer:
[tex] \frac{ - 81}{35} [/tex]
solution
[tex] \frac{9}{7} \times \frac{ - 9}{5} \\ = \frac{9 \times ( - 9)}{7 \times 5} \\ = \frac{ - 81}{35} [/tex]
hope this helps..
Good luck on your assignment
Answer:
-81/35 or -2 11/35
Step-by-step explanation:
Multiply the numerators together. Multiply the denominators together. Then reduce if possible. Also, since you have positive and negative, the product is negative.
9/7 * (-9/5) = -81/35
As a mixed numeral, it is
-2 11/35
What is the approximate value of x in the diagram below? use one of the trigonometric ratios in the table.
Answer:
x = 31.64
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 36 = 23/x
x tan 36 =23
x = 23/tan 36
x=31.63686382
Rounding to 2 decimal places
x = 31.64
Answer:
D. 31.64
Step-by-step explanation:
Algebraically find the point where the cable and the strut intersect. Interpret your answer. (10 points)
Answer:
√2x+8=x-8
2x+8=x^2-16x+64
-x^2+18x-56=0
x^2-18x+56=0
x(x-4)-14(x-4)=0
(X-4)(x-14)=0
x=4(extraneous) ,x=14
—> x=14
Step-by-step explanation:
Answer: (14,6)
Step-by-step explanation:
Right on edg 2022.
Abe is going to plant 54 oak trees and 27 pine trees.
Abe would like to plant the trees in rows that all have the same number of trees and are made up of only
one type of tree.
What is the greatest number of trees Abe can have in each row?
Answer:
27 trees
Step-by-step explanation:
Both numbers are divisible by 27. For the oak trees there would be 2 rows and for the pine trees there would be 1 row, each made up of 27 trees.
Answer: 27 trees
Step-by-step explanation:
in order to know how many trees Abe can have in each row, we need a number that is a factor of 54 and 27, so that trees ans the 27 pin e trees can be divided up into equal rows.
So, if each row had 9 trees, there would be 54 ÷ 9 = 6 rows of oak trees and 27 ÷ 9 = 3 rows of pine trees. This creates equal rows, but it isn't greatest common factoe of 54 and 27.
To do so, let's find factors 54 and 27
54: 1, 2, 3, 6, 9, 18, 27, 54,
27: 1, 3, 9, 27,
The greatest common factor of 54 and 27 is 27. In math natation this looks like:
gcf (54, 27) = 27
the greatest number of trees that Abe can have in each row is 27
Jeremy and Arnold are working on a project for math class in which they are to identify the quadratic equation that represents a rain gauge that sits off the ground. Graph each of the equations and then determine which one could represent the position of the rain catcher that sits above the ground. The x-axis represents the ground. 1. y = x2 + 11x + 24 2. y = –x2 – 6x – 8 Direction of Parabola: ______ Direction of Parabola: ______ Location of vertex with respect Location of vertex with respect to the x axis: _____________ to the x axis: _____________ Determine if the graph depicts Determine if the graph depicts the rain gauge. ___________ the rain gauge. ___________ Why or why not? ___________ Why or why not? ___________ _________________________ _________________________ _________________________ _________________________ 3. y = x2 – 2x + 3 4. y = x2 + 4x + 4 Direction of Parabola: ______ Direction of Parabola: ______ Location of vertex with respect Location of vertex with respect to the x axis: _____________ to the x axis: _____________ Determine if the graph depicts Determine if the graph depicts the rain gauge. ___________ the rain gauge. ___________ Why or why not? ___________ Why or why not? ___________ _________________________ _________________________ _________________________ _________________________ 5. y = 3x2 + 21x + 30 Direction of Parabola: ______ Location of vertex with respect to the x axis: _____________ Determine if the graph depicts the rain gauge. ___________ Why or why not? ___________ _________________________ _________________________
Answer: see below
Step-by-step explanation:
Given ax² + bx + c = 0
If a > 0 (positive), then parabola opens UP
If a < 0 (negative), then parabola opens (DOWN)
Axis of Symmetry: [tex]x=\dfrac{-b}{2a}[/tex]
Max/Min: Plug axis of symmetry into the given equation and solve for y.
1) y = x² + 11x + 24
a=1 b=11
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(11)}{2(1)}=\dfrac{-11}{2}=-3.5\\\\\\\text{Minimum:}\quad y=(-3.5)^2+11(-3.5)+24 = -6.25[/tex]
2) y = -x² - 6x - 8
a=-1 b=-6
a< 0 so parabola opens DOWN
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(-6)}{2(-1)}=\dfrac{6}{-2}=-3\\\\\\\text{Maximum:}\quad y=(-3)^2-6(-3)-8 = 1[/tex]
3) y = x² - 2x + 3
a=1 b=-2
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(-2)}{2(1)}=\dfrac{2}{2}=1\\\\\\\text{Minimum:}\quad y=(1)^2-2(1)+3 = 2[/tex]
4) y = x² + 4x + 4
a=1 b=4
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(4)}{2(1)}=\dfrac{-4}{2}=-2\\\\\\\text{Minimum:}\quad y=(-2)^2+4(-2)+4 = 0[/tex]
5) y = 3x² + 21x + 30
a=3 b=21
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(21)}{2(3)}=\dfrac{-21}{6}=-3.5\\\\\\\text{Minimum:}\quad y=3(-3.5)^2+21(-3.5)+30 = -6.75[/tex]
Explain how to find the surface area of a can of fruit with a height of 80 mm and a diameter of 60 mm.
Answer:
Just multiply 60 by 80
Step-by-step explanation:
the trainer wants to plan better. she goes to the store on the day she ran out of the first type of dog food. she decides to hug enough dog food to last 90 days. Knowing what she already has in the house how much more of each type of dog food does she need to buy in order to use up all the food in 90 days?
Answer: fciycfuxurxr
Step-by-step explanation:
Yddyxrusstxtsxdyxur
For her birthday, Samantha received a gift card, with a value of $200, to a department store. She wants to purchase at least 5 articles of clothing for work. At the store, sweaters cost $24.49 each and dress pants cost $36.99 each. If Samantha does not spend more than the amount on the gift card, which system of inequalities could be used to determine the number of sweaters, s, and the number of dress pants, p, she can buy? A. s + p $200 B. s + p > 5 $24.49s + $36.99p 5 $36.99s + $24.49p < $200
Answer:
The correct system of inequalities is:
[tex]\left \{ {{s + p \geq 5} \atop {24.99s + 36.99p \leq 200}} \right.[/tex]
Step-by-step explanation:
Since Samantha wants to buy at least 5 pieces of clothing, this means that the total of clothing she buys can be 5 or more, then the sum of sweaters and dress pants she have to buy is:
[tex]s + p \geq 5[/tex]
She can't spend more than the gift card, this means that the number of clothing pieces she buys multiplied by its cost must be less or equal to the card's value, so she has to spend:
[tex]24.99*s + 36.99*p \leq 200[/tex]
Therefore the correct system of inequalities is:
[tex]\left \{ {{s + p \geq 5} \atop {24.99s + 36.99p \leq 200}} \right.[/tex]
Help ASAP. what is this asking me to do
Answer:
It's asking you to write the function in a factored form for example g(x) or f(x) that's why its asking for you to use the x as the variable.
Step-by-step explanation:
PLs help me pls ssssssssssssssssss
Answer:
The answer is p/6-4/5.
hope it helps
Answer:
no
Step-by-step explanation:
how can you tell that 4:1 and 12:3 are equivalent ratios?
Answer:
They are equivalent.
Step-by-step explanation:
You can tell because 4:1 can go into 12:3.
If you multiply 4 by 3 you will get 12.
If you multiply 1 by 3 you would get 3.
12:3=4:1
Hope this helps!
Step-by-step explanation: Two ratios are equal if the fractions that represent the are equal.
So we first write the ratios 4 : 1 and 12 : 3 as the fractions 4/1 and 12/3.
Now, to determine whether the two fractions are equal,
we write each fraction in lowest terms.
Notice that 4/1 or 4 is already in lowest terms.
So let's move on.
12/3 can be simplified to 4.
So we have 4 = 4 which is true.
So that's how we know the ratios 4 : 1 and 12 : 3 are equal.
Find the vertex of the function given below.
y= x2 - 6x +1
Answer:
V( 3, -8 )
Step-by-step explanation:
Parable equation is of the form:
( x - h )² = 4p*(y - k)
In that expression, vertex has coordinates V ( h, k )
Then all we have to do is transform the given equation
y = x² - 6x + 1 or x² - 6x = y - 1 (1)
We can get a perfect square trinomial in the first member of the equation according to:
x² - 6x = ( x - 3 )² - 9
(x - 3 )² = x² - 6x + 9
By substitution en equation (1)
( x - 3 )² - 9 = y - 1
( x - 3 )² = y -1 + 9
( x - 3 )² = y + 8
( x - 3 )² = (y + 8 )
Then vertex coordinates are
V( 3 , -8)
The quotient is ??
The remainder is ??
Answer:
The quotient is 10x + 16
The remainder is 28x² + 10x + 22
Step-by-step explanation:
x³ - 3x² + x - 2) 10x⁴ - 14x³ - 10x² + 6x - 10 (10x + 16
10x⁴ - 30x³+ 10x² - 20x
16x³ - 20x² + 26x - 10
16x³ - 48x² + 16x - 32
28x² + 10x + 22
Therefore, the quotient is 10x + 16
The remainder is 28x² + 10x + 22