Answer:
1/10
Step-by-step explanation:
there are 10 cards, numbered 1 through 10, there is one "5" card. so that's 1 card out of 10 cards, therefore a 1/10the chance or a 10% chance you'll get a 5 (or any specific number)
PLEASE HELP! Manufacturers often alter different packages to save money and to grab customers attention. Explain using an example, how changes in the dimensions of common geometric shapes will affect the volume of the following shapes: prisms, cylinders, cones and spheres.
Answer:
An example of a prism could be a an amazon box to represent a rectangular prism. As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.
An example of a cone would be an ice cream cone. As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.
An example of a cylinder could be a cup. As the height or the radius of the cup increases, the larger the volume. More drink for you.
An example of a sphere would be a soccer ball. As the radius increases, the volume of the ball increases. Hence, larger soccer balls have a bigger radius than smaller soccer balls. This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).
Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.
Step-by-step explanation:
Let's simply look at the equations of each shape.
Volume of a prism = base * height
Volume of a cone = Pi * r^2 * (height/3)
Volume of a cylinder = Pi * r^2 * height
Volume of a sphere = (4/3) Pi r^3
Notice that the volumes of prisms, cones, and cylinders directly correlate to height. As height increases, the volume increases. The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius. Consider if you expanded the radius of the sphere, the volume will increase.
Answer:
Increase or decrease the dimensions of objects. See below for an explanation!
Step-by-step explanation:
An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.
A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.
An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.
A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.
You may also shrink the dimensions for each of these objects to make them smaller.
Hope this helps!
Find the equation of the line.
Answer:
y = [tex]-\frac{1}{3}x+5[/tex]
Step-by-step explanation:
Let the equation of the given line is,
y = mx + b
where 'm' = slope of the line
b = y-intercept of the line
Since slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is represented by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
If the points are (0, 5) and (-3, 6),
Slope of the line 'm' = [tex]\frac{6-5}{-3-0}[/tex]
= [tex]-\frac{1}{3}[/tex]
y-intercept of the line 'b' = 5
Therefore, equation of the given line will be,
y = [tex]-\frac{1}{3}x+5[/tex]
Zero product property
x(2x+4)(x+5)=0
A) x=0, x=-2, X=-5
B) x=0, x=2, x=5
C) x greater than or equal to 0
D) x=-2, x=5
Answer:
A
Step-by-step explanation:
Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.
A submarine is only allowed to change its depth be Racing toward the surface in 60 meter stages. If the submarine starts off at 340 meters below sea level, what is its depth after 4 stages of rising to surface
Answer:
[tex]Depth = 100m[/tex]
Step-by-step explanation:
Given
Initial Level = 340 m
Number of stages = 4
Difference in each stage = 60 m
Required
Determine the depth of the submarine after 4 stages
First, we have to calculate the total distance moved towards the surface of the sea;
This is calculated as
[tex]Total\ Distance = Number\ of\ Stages * Difference\ in\ each\ stage[/tex]
[tex]Total\ Distance = 4 * 60m[/tex]
[tex]Total\ Distance = 240m[/tex]
This implies that the submarine moved a total distance of 240 metres;
It;'s new depth is calculated as follows;
[tex]Depth = Initial\ Depth - Total\ Distance[/tex]
[tex]Depth = 340m - 240m[/tex]
[tex]Depth = 100m[/tex]
Hence, its new depth after 4 stages of rising is 100m
I been stuck on this question for the longest please help
Answer: C. [tex]\sqrt{9} * \sqrt{4}[/tex]
Step-by-step explanation:
There is a square root rule that states [tex]\sqrt{x*y} = \sqrt{x} * \sqrt{y} \\[/tex]
We can apply this rule to this problem.
Given [tex]\sqrt{9*4}[/tex]
We can use the rule to make it equal to [tex]\sqrt{9} * \sqrt{4}[/tex]
This is answer choice C.
Answer: c
Step-by-step explanation: 9*4=36 36* 36 = 1296
9 * 9 = 81 4 * 4 = 16 81 * 16 = 1296 hope this helps
pleaz!!! some body help with number #4 at the bottom
Answer:
See my explanation
Step-by-step explanation:
-2x + (x - 4) = 18
-x - 4 = 18
-x = 22 <- this is wrong in question writing as x = 22
so, x = -22
Determine whether the study is an observational study or an experiment.
Research is conducted to determine if there is a relation between hearing loss and exposure to mumps. Does the description correspond to an observational study or an experiment?
Researchers are observing those with mumps to see how it affects hearing loss at all. There may be strong correlation, weak correlation, or no correlation at all.
With an experiment, researchers would break the participants into two groups: control group and treatment group. Those in the control group get the placebo (fake treatment) while the treatment group gets the treatment applied to them. If we were dealing with an experiment for this context, then the treatment group would get exposed to mumps on purpose. Of course, this is unethical and dangerous so an experiment for this type of project is not a good idea. It's better to go with an observational study.
: Resolver el sistema de ecuaciones por el método de reducción. -x + 3y = 6 x + y = 2
Answer:
[tex]x=0\\y=2[/tex]
Step-by-step explanation:
El método de reducción también llamado Suma y Resta, consiste en multiplicar una o ambas ecuaciones de tal manera que los coeficientes de una de las incógnitas sean iguales y de signo contrario, de tal forma que se eliminen al sumar las ecuaciones.
Nuestras ecuaciones son:
[tex]-x+3y=6\\x+y=2[/tex]
En este caso podemos observar que x y -x son iguales y de signo contrario así que no tendremos que multiplicar y podemos sumar ambas ecuaciones.
Al sumarlas tenemos que:
[tex]4y=8\\y=2[/tex]
Ahora sustituímos el valor que encontramos de y en la segunda ecuación para poder obtener el valor de x.
[tex]x+y=2\\x+2=2\\x=2-2\\x=0[/tex]
Por lo tanto, x = 0 y y = 2
Ginnie plans to paint a wall. She measures its height and width. She finds that she needs enough paint to cover 8 square meters. Which measurement does 8 square meters represent?
Answer:
The 8 square meters represent the product of the height by the width of the wall and therefore, its area.
Step-by-step explanation:
Ginnie is going to paint a wall and measures the height and the width, the walls are usually in the form of a rectangle or square. To find the area of both we need to multiply the height by the width (in the case of the square both are the same) and this will give us the total amount of paint that we need to paint the wall.
In this example, Ginnie finds that she needs enough paint to cover 8 square meters, therefore, these 8 square meters represent the product of the height by the width (that we don't know but it doesn't matter) of the wall and therefore, its area.
ASAP!!! Please help me with this question!!!!!
r = radius
h = r+12 = height, 12 more than the radius
[tex]V = \text{Volume of cone (oblique or not)}\\\\V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*r^2*(r+12)\\\\V = \frac{1}{3}\pi*r^2*r+\frac{1}{3}\pi*r^2*12\\\\V = \frac{1}{3}\pi*r^3+\frac{1}{3}*12\pi*r^2\\\\V = \frac{1}{3}\pi r^3+4\pi r^2\\\\[/tex]
Answer: Choice BANSWER: SECOND OPTION
Marta Fuentes had a balance of $1,200.50 in her checking account. The bank issued her a credit of
$505 and charged her $12 for new checks. Thee will be no outstanding checks or deposits. What
should her checkbook balance be?
Answer:
$683.50Step-by-step explanation:
Initial balance of Marta Fuentes = $1200.50
Charge made by her bank;
Credit of $505 and Charge on new checks is $12.
Total charge incurred = $505+$12
Total charge incurred = $517
Since there will be no outstanding checks or deposit, her checkbook balance will be the difference between the initial balance and amount charged by the bank.
Checkbook balance = $1200.50 - $517
Checkbook balance = $683.50
Hence her checkbook balance should be $683.50
PLSSSS HELPPP. The price of a tennis racquet is inversely proportional to its weight. If a 20 oz. racquet cost $30.00, what would a 25 oz. racquet cost?
Answer:
$24 will be the cost of tennis racquet with weight 25 oz.
Step-by-step explanation:
Given that Price of racquet is inversely proportional to its weight.
i.e.
[tex]Price \propto \dfrac{1}{Weight}[/tex]
We can replace the proportional sign with a constant of proportionality.
[tex]Price = \dfrac{C}{Weight}[/tex]
Where C is a constant named as constant of proportionality.
Given that cost of 20 oz. racquet is $30.00
Putting both the values :
[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]
So, the equation becomes:
[tex]Price = \dfrac{600}{Weight}[/tex]
Now, we have to find the price of 25 oz. racquet.
Putting Weight = 25 oz and finding Price:
[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]
So, $24 will be the cost of tennis racquet with weight 25 oz.
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A.6
B.7
C.3
D.4
E.5
=======================================================
Explanation:
The distribution is perfectly symmetrical about the center 6. Notice how the left side is a mirror copy of the right side, due to the heights being the same. Because of this, the mean, median and mode are all the same value and that is 6. The mode is equal to 6 as this is the most frequent value.
The longer way to do this problem is to add up each value shown. We have four copies of '2', six copies of '3', and so on. The total sum you would get is 372. Divide this over 62 because there are 62 smaller green squares. The final result is the mean of 6.
The number closest to the mean of the given distribution is 6. Therefore, option A is the correct answer.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
From the given histogram,
Number Frequency
2 4
3 6
4 7
5 9
6 10
7 9
8 7
9 6
10 4
Here, the mean = [2(4)+3(6)+4(7)+5(9)+6(10)+7(9)+8(7)+9(6)+10(4)]/[4+6+7+9+10+9+7+6+4]
= [8+18+28+45+60+63+56+54+40]/62
= 372/62
= 6
Therefore, option A is the correct answer.
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Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x= y=
Answer:
x = 10 units, y = 5 units
Step-by-step explanation:
Given triangle ABC is a 30-60-90 triangle,
m∠C = 60°
By applying Sine rule in the given triangle,
Sin(60)°= [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° [tex]=\frac{\text{AB}}{\text{AC}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{AB}}{\text{AC}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{5\sqrt{3}}{x}[/tex]
x = 10 units
Similarly, by applying Cosine rule in the given triangle,
Cos(60)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
Cos(60)° = [tex]=\frac{\text{BC}}{\text{AC}}[/tex]
[tex]\frac{1}{2}=\frac{y}{x}[/tex]
y = [tex]\frac{x}{2}[/tex]
y = 5 units
Therefore, x = 10 units and y = 5 units will be the answer.
Find the value.
X3-4 when x=3
PLEASE HELP!!! ASAP!!!
Answer:
23
Step-by-step explanation:
Raise 3 to the power of 3
27 - 4
Subtract 4 from 27
23
Hope this was correct
Answer:
23
Explanation:
step 1 - rewrite the expression with the value of x
[tex]x^3 - 4[/tex]
[tex](3)^3 - 4[/tex]
step 2 - solve the exponent
[tex](3)^3 - 4[/tex]
[tex]27 - 4[/tex]
step 3 - subtract
[tex]27 - 4[/tex]
[tex]23[/tex]
therefore, the value of the expression is 23.
the product of two rational number is -10/9. If one of the number is -5/27 ,find the other.
Answer:
Step-by-step explanation:
Let the unknown number = x
[tex]x *\frac{-5}{27}=\frac{-10}{9}[/tex]
x = [tex]\frac{-10}{9}[/tex] ÷ [tex]\frac{-5}{27}[/tex]
[tex]x=\frac{-10}{9}*\frac{-27}{5}\\\\\\x=-2* - 3\\x = 6[/tex]
Which statement(s) is(are) true about cones? Statement 1: A cone has a triangular base. Statement 2: A cone is 3 times larger than a cylinder with the same height and radius. Statement 3: A cone is one-third the size of a cylinder with the same height and radius. Statement 4: A cone has a circular base.
Answer:
Statement 3: A cone is one-third the size of a cylinder with the same height and radius.
Statement 4: A cone has a circular base.
Step-by-step explanation:
Statement 3: A cone is one-third the size of a cylinder with the same height and radius.
Statement 4: A cone has a circular base.
The true statement is:
Statement 3: A cone is one-third the size of a cylinder with the same height and radius.
Statement 4: A cone has a circular base.
What is Cone?A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top . A cone has one face . There are no edges for a cone.
Properties of Cone
A cone is a shape that has a curved surface and a circular base. The following properties of a cone help us identify it easily. They are as follows.A base of a cone is circular.There is one face, one vertices, and no edges for a cone.The slant height of a cone is the length of the line segment joining the of the cone to any point on the circumference of the base of the cone.A cone have circular base at a perpendicular distance is called a right circular cone.A cone have circular base is an oblique cone.As, from the properties of cone we can say that.
A cone is one-third the size of a cylinder with the same height and radius. and, : A cone has a circular base..
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Devi’s mother is three times as old as Devi. Five years ago, Devi’s mother was four times as old as Devi was then. Find their present ages
Answer:
Devi's present age = 15 years
Devi's Mother's present age = 45 years
Step-by-step explanation:
Let the present age of Devi be x years.
Therefore, mother's present age = 3x
Five years ago:
Devi's age = (x - 5) years
Mother's age =( 3x - 5) years
According to the given condition:
Five years ago:
Devi's mother's age = 4 times Devi's age
3x - 5 = 4( x - 5)
3x - 5 = 4x - 20
20 - 5 = 4x - 3x
15 = x
x = 15 years
3x = 3* 15 = 45 years
Hence,
Devi's present age = 15 years
Devi's Mother's present age = 45 years
PLZZZZZZ HELP I NEED IT I AM GOING TO FAIL PLZZZZ I AM COUNTING ON YOU For which situations is it appropriate to use a sample? Select three options. A. What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck? B. What is the average number of rainbows each year in Honolulu? C. How many pedestrians would use a walkway built over a busy road? D. How many police cars are equipped with computers? E. What is the most popular car color in the teachers’ parking lot?
Answer:
b-What is the average number of rainbows each year in Honolulu?
c-How many pedestrians would use a walkway built over a busy road?
d-How many police cars are equipped with computers?
this is the answer
Step-by-step explanation:
E D G E N U I T Y
The situations it is appropriate to use a sample:
B. What is the average number of rainbows each year in Honolulu?
C. How many pedestrians would use a walkway built over a busy road?
D. How many police cars are equipped with computers?
What is a simple sample technique?Simple random sampling is a sampling technique in which each member of a population has an equal chance of being chosen, through the use of an unbiased selection method. The sample is chosen by a random method as every subject in the sample is assigned a number.
Why do we use sampling techniques?Sampling saves money by granting researchers to gather the same answers from a sample that they would receive from the population. Non-random sampling is significantly cheaper than random sampling because it lowers the cost associated with searchinh people and collecting data from them.
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Which set of ordered pairs represents a function?
{(-3,4), (-7,2), (-7,-4),(-9, -5)}
{(-2,4), (0,5),(-9,9),(-9,7)}
{(-4,-6), (-7, -5),(-4,-7), (1,1)}
{(5,-2), (-8,-6),(4, -2), (-6,3)}
Answer:
The correct answer is D.
Step-by-step explanation:
A function is when an input value has only one output value.
It cannot be A, because -7 produces both 2 and -4.
It cannot be B, because -9 produces both 9 and 7.
It cannot be C, because -4 produces both -6 and -7.
Therefore, it has to be D.
Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8
Answer:
b=4
Step-by-step explanation:
So, we have the function [tex]f(x)=1/x[/tex]. We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).
f(2) = 1/(2) = 1/2
So, we have the point (2, 1/2)
At point b, f(b) = 1/b.
Let's plug this into the slope formula:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8[/tex]
Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).
[tex]\frac{.5b-1}{2b-b^2} =\frac{-1}{8}[/tex]
Now, cross multiply.
[tex]4b-8=b^2-2b[/tex]
[tex]b^2-6b+8=0[/tex]
Solve for b. Factor using the numbers -4 and -2.
[tex]=(b-4)(b-2)=0[/tex]
Thus, b=4 or b=2.
However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.
We want to find an interval such that the given equation, f(x) = 1/x, has an average rate of change of -1/8 in that interval.
We will see that the interval is [2, 4]
-------------------------------
For a function f(x), the average rate of change in the interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Here we have:
[tex]f(x) = 1/x[/tex]
And the interval is [2, b] such that r in that interval is -1/8, so we need to solve:
[tex]r = -1/8 = \frac{f(b) - f(2)}{b - 2} = \frac{1/b - 1/2}{b - 2}[/tex]
We can rewrite it to:
[tex]-1/8 *(b - 2)= 1/b - 1/2\\\\-1/8 *(b - 2)= 2/2b - b/2b = (2 - b)/2b = -(b - 2)/2b[/tex]
Now we can remove the term (b - 2) because it appears on both sides, so we get:
[tex]-1/8 = -1/2b\\1/8 = 1/2b\\2/8 = 1/b\\1/4 = 1/b\\b = 4[/tex]
Then we found that b must be equal to 4, so the interval is [2, 4]
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The formula for working out the cost of hiring a canoe is : cost=£15+6* number of hours. Megan paid £27 to hire a canoe. How long did she hire the canoe for
Answer:
Megan hired the canoe for 2 hours
Step-by-step explanation:
Given:
Cost(h) = 6h+15 = 27
Solution
6h+15 = 27
6h = 27-15 = 12
h = 2
Callie has a new kitten. The kitten weighs 3 pounds less than half the weight of Callie’s cat. Together, the cat and the kitten weigh 18 pounds. Which system of equations could be used to find the weight of each animal?
Answer:
y = [tex]\frac{1}{2} x - 3[/tex]
x + y = 18
Step-by-step explanation:
Let the kitten's weight be y and the cat's weight be x
Condition # 1:
y = [tex]\frac{1}{2} x - 3[/tex]
Condition # 2:
x + y = 18
i attached the question in the image below
Answer:
45°
Step-by-step explanation:
[tex]tan^{-1}(1)[/tex] = 45°
Answer:
[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]
Step-by-step explanation:
[tex]\tan\theta=1[/tex]
[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]
precalc! how do you solve by completing the square? i have 2 examples! (17 & 18 please) tysm <3
Answer:
17) x = 11, -8
18) exact form: x = + 2 sqaure root 6/ 3 + 2
I hope this helps :)
Solve the equation by completing the square.
3x^2-12x=96
Answer:
x = 8
or
x = -4
Step-by-step explanation:
3x² - 12x = 96
Divide both sides by 3
x² - 4x = 32
Add 4 to both sides
x² - 4x + 4 = 32 + 4
(x - 2)² = 6²
Find the square root of both sides
√(x - 2)² = √6²
x - 2 = +/- 6
x - 2 = +6 or -6
x - 2=+6
x=6+2
x=8
x - 2=-6
x=-6+2
x=-4
x = 8
or
x = -4
Find the area in square centimeters of the composite shape shown
below. Enter only a number as your answer.
A
E
13 cm
D
11 cm
7 cm
B
18 cm
C
Answer:
73cm²
Step-by-step explanation:
Area of rectangle=½ length×width
=½×18×7
=63cm²
Area of triangle=½b×h
base=18-13= 5cm
height=11-7 =4cm
½×b×h
½×5×4
=10cm²
Area of total=63+10
73cm²
Answer: 73c2
Step-by-step explanation:
True or False? All equiangular triangles are similar.
Answer:
True
Step-by-step explanation:
All equiangular triangles are similar.
Pleas answer this question now
Answer:
[tex]x = 17[/tex]
Step-by-step explanation:
According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.
That is, [tex]x + 4 = 21[/tex]
Solve for x
[tex]x + 4 = 21[/tex]
Subtract 4 from both sides
[tex]x + 4 - 4 = 21 - 4[/tex]
[tex]x = 17[/tex]
Tonia and trinny are twins. Their friends give them identical cakes for their birthday. Tonia eats 1/8 of her cake and trinny eats 1/6 of her cake. How much cake is left? please show working thank youu
Answer:
[tex]\frac{7}{12}[/tex] of the cake
Step-by-step explanation:
add [tex]\frac{1}{8}[/tex] and [tex]\frac{1}{6}[/tex] to see the total amount of cake eaten.
a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24
b. multiply accordingly to get the correct numerator: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex]
c. add: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex] = [tex]\frac{7}{24}[/tex]
subtract found value from total to find left over cake.
a. 24 - 7 = 14
simplify.
a. [tex]\frac{14}{24}[/tex] = [tex]\frac{7}{12}[/tex]
You are left with [tex]\frac{7}{12}[/tex] of the cake.