Whole numbers are similar to natural(non-negative, non-fractional). The only difference is that it includes the 0.
In this question, Rio placed -1 as an example of whole number. Since -1 is negative, it is not a whole number, so this the number which Rio placed incorrectly.
Find the percent of change from 80 kmph to 60 kmph
33.3% increase
25% increase
25% decrease
33.3% decrease
The most appropriate choice for Percentage will be given by
There is a 25 % decrease in speed
3rd option is correct
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. Then that number is called percentage.
For example, 2% means [tex]\frac{2}{100}[/tex]
Original speed = 80 kmph
New speed = 60 kmph
Decrease in speed = (80 - 60) kmph
= 20 mph
Percentage decrease = [tex]\frac{20}{80} \times 100\\[/tex]
= 25 %
There is a 25% decrease in speed.
3rd option is correct
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Use the following situation to complete Exercise 7. 7. The school photography club charges $10 for each photo in its annual pet photolontest. The club wants to save $75 of its earnings for a pizza party. The club members also want to have at least $50 left over after the pizza party to pay for other club expenses. Write an expression for: a. how much money the club earns by taking p pet photos
Answer:
10p
Explanation:
We are told that the photography club charges $10 for each photo; therefore, if we have p number of photos then the total amount charged will be 10 * p = 10p
An artist mixes yellow and blue paint to make the perfect shade of green.she uses 2 ounces of blue paint for every 7 ounce of yellow. How many ounces of yellow will the artist need to add to 12 ounces of blue
Describe how CPCTC would help you here. (8x-6) D T Students DE VOLTRON
CPCTP = Corresponding parts of congruent triangles are congruent:
That means that since both angles are congruent (equal) the sides are also congruent:
8x+6 = 3x+9
Solve for x
8x-3x = 9-6
5x= 3
x= 3/5
Write the augmented matrix for the following system of equations.
9y-5+9z = 0
7x=-3y+7+z
5x + 7y = 5
The augmented matrix of the given equations is shown (Refer to the matrix attached below.)
What is an augmented matrix?An augmented matrix in linear algebra is a matrix created by joining the columns of two given matrices, typically so that the same basic row operations can be applied to each of the given matrices individually. An augmented matrix for a system of equations is a matrix of numbers where each column represents all the coefficients for a single variable and each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign).So, the augmented matrix will be:
Equations are,
9y-5x+9z = 07x=-3y+7+z5x + 7y = 5Rewrite them systematically as:
-5x + 9y + 9z = 07x + 3y - z = 75x + 7y + 0 = 5Now, augmented matrix:
(Refer to the matrix attached below)Therefore, the augmented matrix of the given equations is shown (Refer to the matrix attached below.)
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A triangle on a coordinate plane is translated according to the rule T-8, 4(x, y). Which is another way to write this rule?
(x, y)
(x + 4, y-8)
(x-4, y-8)
O(x, y)
O (x,y) - (x-8, y + 4)
O(x, y) (x+8, y-4)
A triangle coordinate translate T-8, 4(x, y). Then we can rewrite the translation rule as :
( x, y ) → ( x - 8, y + 4).
Solution:A translation is a type of transformation in which every point in a figure moves the same distance in the same direction. Slides are another term for translations. A translation can be described using words like "moved up 3 and over 5 to the left" or with notation.The function translation / transformation rules are as follows: f (x) + b raises the function by b units. The function f (x) b is shifted downward by b units. f (x + b) moves the function to the left by b units.Here we know that according to the translation rule Ta,b( x , y) the translation of a point (x,y) by (a,b) is given by:
(x , y) → ( x + a , y + b)
The following statement is true: A triangle on a coordinate plane is translated according to the rule.
T₋₈ , ₄(x , y).
Then, another way to write this rule is:
( x , y) → (x + (-8) , y + (4))
( x, y ) → ( x - 8, y + 4).
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(1/5+1/2 to the 2nd power)+3/10x5
The value of this given algebraic addition is 51/100.
The problem is in sentence format, we have to convert this to a mathematical format.
We can find the value of these given mathematical digits by following a few steps.
1/5 + ( 1/2 )^2 + 3/10×5
= 1/5 + 1/4 + 3/50 = 40/ 200 + 50/200 + 12/200
( we have multiplied both denominator and nominators with different numbers to assure that denominator of all numbers is the same )
= 102/200 ( here we have divided both with 2, to minimize the given fraction )
= 51/100.
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The length, x (in inches), and weight, y (in ounces), for
a type of bass were measured for a random sample of
10 bass from a lake. These measurements were then
analyzed and the value for 2 was determined to be
96%.
Which of the following is the best interpretation of this
value?
4% of the variation in the bass's length is
determined by the variation in the bass's weight.
O 96% of the variation in the bass's weight is
determined by the variation in the bass's length.
96% of the variation in the bass's length is
determined by the variation in the bass's weight.
98% of the variation in the bass's weight is
determined by the variation in the bass's length.
Best interpretation of the value of 96% is that there is a strong positive linear relationship between the length and weight of the bass in the sample
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
The value of 96% refers to a correlation coefficient, which measures the strength of the linear relationship between two variables. In this case, the two variables are length (x) and weight (y) of a type of bass. A correlation coefficient of 96% indicates a very strong positive correlation between the two variables, meaning that as the length of the bass increases, its weight tends to increase as well.
However, the value does not provide information about causality or which variable is influencing the other.
Therefore, none of the given interpretations are accurate. Instead, the best interpretation of the value of 96% is that there is a strong positive linear relationship between the length and weight of the bass in the sample, and further analysis may be needed to determine the direction and strength of causality between the two variables.
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complete the two way relative frequencies using decimels, and round to three places.
To complete the second table, you need to divide all cells in the first table by 41. obtaining:
Hits to a high-volume Web site are assumed to follow
a Poisson distribution with a mean of 10,000 per day.
Approximate each of the following:
(a) The probability of more than 20,000 hits in a day
(b) The probability of less than 9900 hits in a day
(c) The value such that the probability that the number of hits
in a day exceeds the value is 0.01
(d) Approximate the expected number of days in a year (365
days) that exceed 10,200 hits.
(e) Approximate the probability that over a year (365 days)
more than 15 days each have more than 10,200 hits
Given the following, (a) 100 (a) 0 (b) 0.1587 (c) 10233 (d) 8.322 (e) 0.0096
How can I tell if the distribution of my data is Poisson?The ratio of variance to mean in a sample in n counts from a distribution with a Poisson coefficient ought to correspond to a Chi-square population with n-1 angles of freedom. This test depends on the fact that the mean and variance of the Poisson distribution are identical.
a)
Here for Poisson distribution
Here mean of distribution=μ=λ= 10000
Variance =σ2=λ= 10000
Standard deviation σ=√λ= 100.000
Considering that λ is big, we can approximate:
a)
Probability of more than 20000 hits in a day:
Probability =P(X>20000)=P(Z>(20000-10000)/100)=P(Z>100)=1-P(Z<100)=1-1=0
if using ti-84 press -2nd -vars - command :normal cdf(20000,1 2nd EE 99,10000,100)
b)
P(less than 9900 hits):
Probability =P(X<9900)=(Z<(9900-10000)/100)=P(Z<(-1)=0.1587
If using ti-84 press 2nd -vars - command :normalcdf(-1 2nd EE 99,9900,10000,100)
c)
For top 0.01 or 99th percentile critical value of z=2.33
Therefore corresponding value=mean+z*std deviation=10233
If using ti-84: press 2nd-vars-invNorm(0.99,10000,100)
d)
Probability of exceeding 10200:
Probability =P(X>10200)=P(Z>(10200-10000)/100)=P(Z>2)=1-P(Z<2)=1-0.9772=0.0228
Therefore expected number of days that exceed 10200 hits =np=365*0.0228=8.322
e)
Mean of distribution=μ=np= 8.3220
and standard deviation σ=sqrt(np(1-p))= 2.8517
For normal distribution z score =(X-μ)/σx
P(more than 15 days has more than 10200 hits):
Probability =P(X>15)=P(Z>(15-8.322)/2.852)=P(Z>2.34)=1-P(Z<2.342)=1-0.9904=0.0096
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which expression represents the sum of 173and32,times by 5
EXPLANATION
The expression that represents the sum of 173 and 32 times by 5 is
(172+32)x5 [OPTION C]
4 - 3(x-3) = 5(x+2) - 8xSolve for the variable in the equation shown
Given:
The equation is,
[tex]4-3(x-3)=5(x+2)-8x[/tex]Simplify the equation,
[tex]\begin{gathered} 4-3\mleft(x-3\mright)=5\mleft(x+2\mright)-8x \\ \text{LHS}=4-3(x-3) \\ =4-3x-3\times(-3) \\ =4-3x+9 \\ =13-3x\ldots\ldots\text{.}\mathrm{}(1) \\ \text{RHS}=5(x+2)-8x \\ =5x+5(2)-8x \\ =-3x+10\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Now,
[tex]\begin{gathered} 13-3x=-3x+10 \\ -3x=-3x+10-13 \\ -3x=-3x-3 \\ \Rightarrow-3=0 \\ \Rightarrow No\text{ solution} \end{gathered}[/tex]2x2 and the times tables
Explanation:
The question asked for
[tex]2\times2,and\text{ }the\text{ }times\text{ }table[/tex]Concept:
2 times 2 means the addition of 2 in 2 places
[tex]\begin{gathered} 2\times2=2+2 \\ 2\times2=4 \end{gathered}[/tex]The time table is given below as
Hence,
The final answer is
[tex]\Rightarrow2\times2=4[/tex]A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table.
Labor-Hours per Ski
Maximum Labor-Hours
Available per Day
Department
Fabricating
Finishing
Trick Ski
6
1
Slalom Ski
4
1
132
30
If the profit on a trick ski is $50 and the profit on a slalom ski is $30, how many of each type of ski should be manufactured each day to realize a maxi
What is the maximum profit?
The maximum profit will be $2,700.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The profit on a trick ski is $50 and the profit on a slalom ski is $30.
Let the number of Trick ski manufactured = x
And, Number of slalom ski manufactured = y
So, Maximize;
P = 50x + 30y
Subject to we get;
6x + 4y ≤ 108
And, x + y ≤ 24
And, xy ≤ 0
Now, We have to find set of feasible solutions graphically for the number of each type of ski that can be produced.
So, Linear equation in slope form;
6x + 4y = 108
y = -1.5x + 27
And, x + y = 24
y = - x + 24
So, By the graph we get;
The points,
(x , y) = (0, 24) , (6 , 18) (18, 0)
Hence, The maximum profit when 6 trick ski and 18 slalom ski manufactured.
maximum profit = 6 x 50 + 18 x 30 = 840
And, The maximum profit when 18 trick ski and 0 slalom ski manufactured.
maximum profit = 18 x 50 = 900
The maximum profit when 0 trick ski and 24 slalom ski manufactured.
maximum profit = 24 x 40 = 960
Thus, The maximum profit = 840 + 900 + 960
= $2,700
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Estimate the total cost of the following items for your dorm room round the individual cost to the nearest $10 round your answer to the nearest dollar (cents)
We will determine the approximate cost as follows:
[tex]149.67+59.58+29.56+19.79=258.60[/tex]So, the total cost would be $258.60.
EspanA parachutist's speed during a free fall reaches 75 meters per second. What Is this speed in feet per second? At this speed, how many feet will the parachutistfall during 20 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.Speed:Distance fallen in 20 Seconds:
The speed of the parachutist is falling is 75m/s.
You have to express the speed of the fall in ft/s.
1m is equal to 3.3ft
To express the speed in ft per second, given that the time unit is the same, you have to multiply 75m/s by 3.3
[tex]75\cdot3.3=247.5[/tex]The speed, expressed in feet per second, is 247.5ft/s
This means that the parachuter falls 247.5ft every second, to determine the distance fallen in 20 seconds, you have to multiply the speed by the time:
[tex]247.5\cdot20=4950[/tex]After 20 seconds he will fall 4950ft
r2/r12 A. r10B. 1/r6C.1/r10D. r8E. r6
this is
[tex]\frac{r^2}{r^{12}}=r^{2-12}=r^{-10}=\frac{1}{r^{10}}[/tex]answer: C
Find the solution to the system of equations. You can use the interactive graph below to find the solution.-2x+2y=-43x+3y=-18x=___y=___
Answer:
• x=-2
,• y=-4
Explanation:
Given the system of equations:
[tex]\begin{gathered} -2x+2y=-4 \\ 3x+3y=-18 \end{gathered}[/tex]Solve for x and y using the graphical method.
The first step is to plot each of the lines using the x and y-intercepts.
First Equation (-2x+2y=-4)
When x=0
[tex]\begin{gathered} 2y=-4 \\ y=-2 \\ \implies(0,-2) \end{gathered}[/tex]When y=0
[tex]\begin{gathered} -2x=-4 \\ x=-\frac{4}{-2} \\ x=2 \\ \implies(2,0) \end{gathered}[/tex]Join the points (0,-2) and (2,0) as shown below:
Second Equation (3x+3y=-18)
When x=0
[tex]\begin{gathered} 3y=-18 \\ y=-6 \\ \implies(0,-6) \end{gathered}[/tex]When y=0
[tex]\begin{gathered} 3x=-18 \\ x=-\frac{18}{3} \\ x=-6 \\ \implies(-6,0) \end{gathered}[/tex]Join the points (0,-6) and (-6,0) on the same graph as shown below:
The solution to the system is the point where the two lines intersect.
The point is (-2,-4).
Therefore:
• x=-2
,• y=-4
,•
how many ice cream servings can the 5 sisters buy if they only want to spend 10.00$ on ice creams. Write an inequality. Ice creams is 2.80$
Let the number of ice-cream serving the sisters can buy be "s".
Each serving is $2.80, so the cost of "s" ice-creams will be:
[tex]2.80s[/tex]This cost cannot exceed 10 dollars.
10 dollars is the maximum.
So, we can say that "2.80s" is equal to or less than 10.
We write it in inequality notation:
[tex]2.80s\leq10[/tex]Solving for "s":
[tex]\begin{gathered} 2.80s\leq10 \\ s\leq\frac{10}{2.80} \\ s\leq3.57 \end{gathered}[/tex]So, the logical solution is that the 5 sisters can buy 3 ice-cream servings with their budget.
If m∠4 = 96 and m∠5 = 138, what is m∠3?
Applying the triangle sum theorem, the measure of angle 3 = 54°.
What is the Triangle Sum Theorem?The triangle sum theorem is the theorem that justifies why the sum of all the interior angles of a triangle is equal to 180 degrees.
Given the following measures:
Measure of angle 4 = 96°Measure of angle 5 = 138°Measure of angle 1 = 180 - m∠4 [linear pair have a sum of 180 degrees]
Substitute
Measure of angle 1 = 180 - 96
Measure of angle 1 = 84°
Measure of angle 2 = 180 - m∠5 [linear pair have a sum fo 180 degrees]
Substitute
Measure of angle 2 = 180 - 138
Measure of angle 2 = 42°
Therefore:
Measure of angle 3 = 180 - m∠1 - m∠2 [triangle sum theorem]
Substitute
Measure of angle 3 = 180 - 84 - 42
Measure of angle 3 = 54°
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Stretch or compress each linear function. Let g(x) be a vertical stretch of f(x)=2x-2 by a factor of 5. Write the rule for g(x).
If g(x) = cf(x), then g(x) is a vertical stretch of f(x) by a factor of c. It means that the rule for g(x) is:
g(x) = 5*f(x)
Replacing f(x) by 2x - 2, we get:
g(x) = 5*(2x - 2)
g(x) = 5*2x - 5*2
g(x) = 10x - 10
Answer: g(x) = 10x - 10
19 students reported seeing the latest blockbuster film over the summer, 76 total students were surveyed. Which fraction represents the ratio of students who saw the movie to total students surveyed?A. 1/4B. 4/15C. 2/7D. 3/7
In this case the answer is very simple. .
We must find the proportion and compare it with the options.
Step 01:
ratio of students who saw the movie
[tex]\frac{\text{students saw the movie}}{\text{total students surveyed}}\text{ = }\frac{19}{76}\text{ = }\frac{1}{4}[/tex]The answer is:
Option A.
Solve on the interval [0,27): 2 cscx -3 = -5 ОА. Зл 2 O 2T 4T B. 3.3 7 T 1 IT c O T O D. IS
Answer:
[tex]x\text{ = }\frac{3\pi}{2}[/tex]Explanation:
We want to get the value of x on the interval for which the identity holds true
We have this as follows:
[tex]\begin{gathered} \csc \text{ x = }\frac{1}{\sin \text{ x}} \\ \\ \frac{2}{\sin \text{ x}}\text{ = -5+3} \\ \\ \frac{2}{\sin \text{ x}}\text{ = -2} \\ \\ \sin \text{ x = -1} \\ \\ x\text{ = }\sin ^{-1}\text{ (-1)} \\ \\ x\text{ = }\frac{3\pi}{2} \end{gathered}[/tex]Understanding Ratios
Eliza is a chef at a restaurant. She is making spaghetti sauce and put 21 tomatoes and 6 onions in the pot. Wh
tomatoes to onions in the pot?
Answer: The Answer is 7:2
Step-by-step explanation:
is 7:2
Which equation is equivalent to 0.05n+ 0.1d = 4.55?
O 5n+d=455
O 0.5n+d=455
O5n+10d=455
0.05d + 0.1n = 455
Answer:
[tex]5n+10d=455[/tex]
Step-by-step explanation:
Multiply both sides of the equation by 100.
Graph the function f(x)=3/2x−4.Use the line tool and select two points to graph.
We are meant to graph the function
f(x)=3/2x − 4.
rewrite the sum in the form a(b+c) such that integers b and c have no common factor
The given format of the sum is
[tex]a(b+c)[/tex]The sum is,
24+16
The greatest common factor of 24 and 16 is 8, since,
[tex]\begin{gathered} 24=12\times2=3\times2\times2\times2 \\ 16=8\times2=4\times2\times2=2\times2\times2\times2 \end{gathered}[/tex]Therefore we can write, 24+16 as,
[tex]24+16\rightarrow8\times3+8\times2=8(3+2)[/tex]Divide the fraction. Express your answer to the nearest tenth. A calculator may be used.0.70.09Enter a number as an exact integer or decimal.eBookSubmit Answer
The given fraction is
[tex]\frac{0.7}{0.09}[/tex]Using a calculator, we have
[tex]\frac{0.7}{0.09}=7.77777777777\ldots[/tex]However, rounded to the nearest tenth would be
[tex]7.7777777777\ldots=7.8[/tex]Therefore, the answer is 7.8.- One leg of a right triangle is 4 inches longer than the other leg. The hypotenuse is 20 inches long. What is thelength of the shortest side?
Let's name the a, b, c
let side a = x
let side b = 4+x
Let side c = hypotenuse = 20
Using the law of pythagoras
opposite² + adjacent² = hypotenus²
x² + (x+4)² = 20²
open the parenthesis
x² + x² + 4x +16 = 400
2x² + 4x + 16 = 400
2x² + 4x + 16 - 400 = 0
2x² + 4x - 384 = 0 --------------------------------(1)
The is now a quadratic equation
so we will solve and find x
Using the formula method
Quadratic formula is
[tex]x\text{ = }\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Comparing equation (1) with ax² + bx + c = 0
a = 2 b = 4 and c= -384
Inserting the values into the formula
[tex]x\text{ = }\frac{-4\text{ }\pm\sqrt{4^2\text{ - 4(2)(-384)}}}{2(2)}[/tex]simplifying the above
[tex]x\text{ = }\frac{-4\pm\sqrt{16\text{ + 3072}}}{4}[/tex][tex]undefined[/tex]Which inequality is true for all real numbers? Check all that apply.
a-b
ac≥ bc
If az b, then a + c≥ b + c
If c> d, then a-c
If a
The inequalities 3 and 4 are the right ones, because they are actually properties of inequalities.
What do math inequalities mean?
inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.Income gap, gender inequality, access to health care, and social class are some of the most prominent instances of social inequality. Some people receive better and more skilled care in the medical field than others.The inequalities 3 and 4 are the right ones, because they are actually properties of inequalities.
The alternate options are incorrect. For instance, the first option, a - b a + b, is false because the expression would be ruined if you don't apply the same adjustment to both sides of the inequality.
Both options 2 and 5 are incorrect.
The proper responses are thus 3 and 4.
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Answer:
3,4
Step-by-step explanation:
