Whole numbers are the numbers 0, 1, 2, 3, 4, etc. (the natural numbers and zero). Negative numbers are not considered whole numbers. All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
For example.
- 2, - 10
A person tosses a coin 14 times. In how many ways can he get 10 heads?
A physician borrowed $100,000 from credit union for 9 months at annual interest rate of 4%. What is the simple interest due on the loan?
Givens.
• The amount borrowed was $100,000.
,• The time elapsed is 9 months.
,• The annual interest rate of 4%.
The simple interest formula is
[tex]I=PRT[/tex]Where P = 100,000, R = 0.04, and T = 9/12.
[tex]\begin{gathered} I=100,000\cdot0.04\cdot\frac{9}{12} \\ I=3,000 \end{gathered}[/tex]Therefore, the simple interest is $3,000.the answer would be 3,000
A bag contains 42 red, 42 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is purple or not red
The probability of a candy when randomly taken is purple or not red is 0.235
Given,
Number of red candies in the bag = 42
Number of green candies in the bag = 42
Number of yellow candies in the bag = 20
Number of purple candies in the bag = 32
We have to find the probability of a candy when randomly taken is purple or not red.
Probability, P(E) = Number of favorable outcomes / Total number of favorable outcomes
Here,
Number of favorable outcomes = 32
Total number of favorable outcomes = 42 + 42 + 20 + 32 = 136
So,
P(E) = 32/136 = 0.235
That is,
The probability of a candy when randomly taken is purple or not red is 0.235
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The graph of y=-2is is transformed to becomey=+5. Which of the folloA The graph is translated Sunits left and 2 units up.& The graph is translated 2 units left and Sunits ups.Oc.thegraph is mamiandumits left and sumits chosam.OD The graph is translated Sunits right and 2 units dow
Given the following function:
[tex]y=\sqrt{x-2}[/tex]notice that the transformation:
[tex]y=\sqrt{x}+5[/tex]can be written like this:
[tex]y=\sqrt{(x+2)-2}+5[/tex]first, the +2 means that the graph moves 2 units left, and the +5 makes the graph move 5 units up.
Hi! I need some help with my precalculus homework question, please. Thank you for your time.
If the point (4, -1) is a point on the graph of f, then f(4) = -1
First blank = 4
second blank = -1
Explanation:The given point: (4, -1)
From the point: the coordinate tells us x = 4, y = -1
For a graph of function f, f(x) is the same as y
To represent the point (4, -1) as a funtion of x (that is f(x)), we will replace x in f(x) with the value of the x coordinate. The result when we replace it will the value of the y coordinate
when x = 4
f(4) = the value of the y coordinate
f(4) = -1
To complete the blanks:
If the point (4, -1) is a point on the graph of f, then f(4) = -1
First blank = 4
second blank = -1
Your account number is 421746. You wish to deposit 120 dimes, 25 quarters, and checks for $184.63 and $196.17. You wish to receive $50.00 in cash. Complete the savings deposit slip.
The deposit slip would look like this:
we have that the currency is 120 dimes = $1.2 and 25 quarters = $6.25.
can u please help me before I get on error message, and It kicks me out the tutoring
To find the image we have to multiply every coordinate by the scale factor.
Then:
[tex]\begin{gathered} A^{\prime}(0,2) \\ B^{\prime}(9,0) \\ C^{\prime}(4,4) \end{gathered}[/tex]describe the general trend of the unadjusted federal minimum wage from 1985 to 2020
From the graph we can infer that the general trend for the unadjusted federal minimum wage has been an increase.
1 yard =3 feet1 meter= 100 cmNicholas walked 20 yards to get his mail. About how many meters did he walk?
Given:
1 yard = 3 feet
1 meter = 100 cm
Nicholas walked 20 yards to get his mail.
Here, we are required to convert 20 yards to meters.
Where,
1 yard = 0.9144 meter
20 yards = x meters
thus, we have:
[tex]20\text{ }\times0.9144\text{ = 18.29 meters}[/tex]Therefore, Nicholas walked 18.29 meters to get to his mail.
ANSWER:
18.29 meters
When solving an equation for x if you get 4=10, that means what?
Given: An equation where
[tex]4=10[/tex]To Determine: the nature of the solution of the equation
Solution
Nature of solution: The example below relates to the nature of solution
[tex]\begin{gathered} Note:4=4(infinitely\text{ many solution\rparen} \\ a=4(one\text{ solution\rparen} \\ 4=10(no\text{ solution\rparen} \end{gathered}[/tex]Hence, the equation has no solution
Compare -2/3 to 3/4 is it equal, less.or greater
Answer:
less
Step-by-step explanation:
negative numbers are less than positive numbers
[tex]-\frac{2}{3} < \frac{3}{4}[/tex]
Hope this helps
I need help with a table to plot the points
In order to plot a set of coordinates on a graph page, you would need to take account of every pair of x and y values provided. The line that goes horizontally is the x-axis (from left to right). All the negative values move from point zero (the origin).
The ordered pair, or the coordinates tells you where x and y intersect. For example, the first set of coordinates are (2, 9). That means, when x is 2, then y is 9.
Observe that x equals 2 on the right side of the horizontal axis. Next, you look for the spot where y equals 9.
Next step, you carefully trace the spot where x is 2, and trace it up a straight line and at the point where y equals 9 (at the upper part of the y axis), you put a tiny "X" to mark the spot where both values intersect.
Notice that while tracing from x, you move upwards, and while tracing from y, you move towards the right. That point defines the coordinates (2, 9) which is the first line on your table.
You follow a similar step for every one of the other coordinates, which are;
[tex]\begin{gathered} (2,9) \\ (4,3) \\ (6,-6) \\ (0,15) \\ (3,6) \\ (5,0) \\ (\frac{7}{3},8) \end{gathered}[/tex]Please note that I've just attached the same graph, but this time I've labelled the points one by one.
This should help with reading the coordinates at every point.
FIRST TO ANSWER ALL GETS BRAINEST
Question 1(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In triangle DEF, m∠D = (3x + 27)°, m∠E = (4x + 22)°, and m∠F = 68°. Determine the degree measure of the exterior angle to ∠D.
54°
58°
122°
126°
Question 2(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In ΔJKL, m∠J = 78° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.
168°
102°
57°
12°
Question 3(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
Triangle UVW is shown with m∠WUV = 36°. The measure of ∠UVW is (5h − 66)°, and the measure of ∠AWB is (5h − 18)°.
triangle UVW with side VW extended through point A and side UW extended through point B, with angle U labeled as 36 degrees
Determine the value of h.
h = 22.8
h = 23
h = 25.4
h = 48
Question 4(Multiple Choice Worth 2 points)
(Interior and Exterior Angles LC)
One interior angle of a triangle is 95.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?
42.25°
47.75°
84.5°
90°
Question 5(Multiple Choice Worth 2 points)
(Interior and Exterior Angles LC)
For ΔABC, m∠A = 28.7° and m∠B = 123.8°. Determine m∠C.
27.5°
62.5°
76.25°
152.5°
Question 6(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.
m∠Y = 22°
m∠Y = 43°
m∠Y = 99°
m∠Y = 158°
Question 7(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
Triangle ABC is shown with exterior ∠z.
triangle ABC with angle A labeled 58 degrees, angle B labeled 44 degrees, and side AC extended with angle z labeled as exterior angle to angle C
Determine m∠z.
136°
102°
78°
58°
The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126° so option (D) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠D + m∠E + m∠F = 180°
(3x + 27) + (4x + 22) + 68 = 180
7x + 49 + 68 = 180
7x = 63
x = 9
So, m∠D = (3(9) + 27)° = 54°.
The exterior angle of D = 180- 54 = 126°.
Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".
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HELP NEEDED ASAP PLS
The expression in the simplest form is -9x/10 + (5).
What is termed as the simplification?Simplify simply means making something easier to understand. Simply or simplification in mathematics refers to reducing an expression / fraction / problem to a simpler form. It simplifies the problem by calculating and solving it.
We can —
Simplify fractions by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This makes this same expression simple to understand and solve.For the given equation;
= (-3x/5 - 7) - (-12 + 3x/10)
open the parenthesis;
= -3x/5 - 7 + 12 - 3x/10
Bring the variable part together.
= -3x/5 - 3x/10 - 7 + 12
Add variables and constant separately.
= -9x/10 + 5
Thus, the simplest form of the given expression is found as -9x/10 + 5.
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if a || b, m<2=63°, and m<9=105°, find the missing measure of m<7=?
Vetical angles are on opposite sides of the intersection of two lines, in this case, when lines c and b intersect, <7 and <9 are formed, these angles are vertical and m<7 = m<9, then:
m<7 = 105°
INVERSES OF AN EXPONENTIAL FUNCTION 6). Fill in the chart. If needed, use a calculator and round to one decimal place.
We will have the following:
x f(x) = 4^x function(x,f(x)) inverse(f(x),x)
0 1 (0, 1) (1, 0)
1 4 (1, 4) (4, 0)
-1 1/4 (-1, 1/4) (1/4, -1)
2 16 (2, 16) (16, 2)
-2 1/16 (-2, 1/16) (1/16, -2)
Answer:
columns in order of 0/1/-1/2/-2
Step-by-step explanation:
g, h and s
e, a and b
d, q and r
k, f and c
m, l and n
Number of Inches in a Mile An inch is approximately1.57828 x 10-5 mile. Find the reciprocal of this num-ber to determine the number of inches in a mile.
We are given that an inch is approximately 1.57828x10⁻⁵ mile.
[tex]1\: inch=1.57828\times10^{-5}\: \text{mile}[/tex]The reciprocal of this number will give us the number of inches in a mile.
[tex]\frac{1}{1.57828\times10^{-5}\: }=63360\: inches[/tex]Therefore, a mile is approximately 63360 inches.
[tex]1\: mile=63360\: \text{inches}[/tex]Which of the following could be the end behavior of f(x) = -x2 – 4?
Answer:
f(x) = -∞ as x → ±∞
Explanation:
The given function is
f(x) = -x² - 4
To know the end behavior, let's replace x by a greater number and by a smaller number, so
If x = 100
f(x) = -100² - 4
f(x) = -10000 - 4
f(x) = -10004
If x = -100
f(x) = -(-100)² - 4
f(x) = -10000 - 4
f(x) = -10004
So, we can see that no matter if x is negative or positive, the value of f(x) will be positive. Then, we can say that the end behavior is
f(x) = -∞ as x → ±∞
Which equation is perpendicularl to 2x+3y=12A y=2/3X+5B y=-2/3X+5C y=3/2X+5D y= -3/2X+5
The equation of the line perpendicular to the given equation is;
[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]Option C is the correct answer
Here, we want to select which of the equations in the option is perpendicular to the given equation
Firstly, we need to understand that for two equations to be perpendicular, then the product of their slopes must be equal to -1
Before we proceed to compare, we need to write the equation in the general form
The equation of the line written in the general form will be;
[tex]y\text{ = mx + b}[/tex]where m represents the slope and the term b represents the y-intercept
Now, let us proceed to write the equation in the standard form;
We have this as;
[tex]\begin{gathered} 3y\text{ = -2x + 12} \\ \\ y\text{ = -}\frac{2}{3}x\text{ + 4} \end{gathered}[/tex]Compared with the general form, we can see that the slope of this line is -2/3
Now let us get the slope of the line that would be perpendicular to it;
[tex]\begin{gathered} \frac{-2}{3}\times\text{ m = -1} \\ \\ m\text{ = }\frac{3}{2} \end{gathered}[/tex]Now, the equation perpendicular to what was given will have a slope of 3/2
Fortunately, all the options in the question have been written in the general form
The one with a slope of 3/2 is option C
[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]determine which of the following relations is a function.Xyxy-1010-32-55-1100025-5110-104O3-8-2124y-4-22346XOx01225y24267
The relation between the function is X cannot repeat itself.
We have given that,
functions table
We have to determine which relation is a function.
What is the function?
A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
The relation between the function is
X cannot repeat itself
Therefore option C is correct.
Complete question: Determine which of the following relations is a function [see in attachment]
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RANGE AND DOMAIN. GRAPSWhat is the Range of this Relation:{(3,0), (-2,6), (-1,4), (-2,0), (1,5)}
Given the relation:
[tex]\mleft\{\mleft(3,0\mright),(-2,6),(-1,4),(-2,0),(1,5)\mright\}[/tex]The range of the relation can be thought of as the set of y-coordinates of a point (x, y). That is, as every second number of the ordered pairs. Additionally, the set should be ordered, and should not contain repeated values. This set is:
[tex]Range=\mleft\lbrace0,4,5,6\mright\rbrace[/tex]True or false?
A "natural monopoly" is a market that runs very inefficiently when one large firm provides all of the output.
The following statement: A "natural monopoly" is a market that runs very inefficiently when one large firm provides all of the output is false.
A natural monopoly is a sort of monopoly that emerges because of the high start-up costs or substantial economies of scale associated with conducting business in a certain industry, which can result in large barriers to entry for potential rivals.
Natural monopolies can form in sectors that require specialized raw resources, technology, or other variables to function. Natural monopolies can also occur when one business is far more efficient than several enterprises in providing the market with the item or service.
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The perimeter of a triangle is 19 inches. One side measures 7 inches. Another side is 5 inches long.Find the length of the third side c.
Statement Problem: The perimeter of a triangle is 19 inches. One side measures 7 inches. Another side is 5 inches long.
Find the length of the third side c.
Solution:
Thus, the perimeter of a triangle with lengths a, b and c is;
[tex]P=a+b+c[/tex][tex]\begin{gathered} \text{Let a=7inches, b=5inches, P=19inches} \\ c=P-a-b \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} c=19-7-5 \\ c=7 \end{gathered}[/tex]Thus, the length of the third side is 7inches
Madison is in the business of manufacturing phones. She must pay a daily fixed cost of $400 to rent the building and equipment, and also pays a cost of $125 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
The equation that represents the total cost is C = $400 + $125p .
What is the total cost?The equation that represents the total cost is a function of the fixed cost and the variable cost. The fixed cost remains constant regardless of the level of output. The variable cost changes with the level of output.
Total cost = fixed cost + total variable cost
Total cost = fixed cost + (variable cost x total output)
C = $400 + ($125 x p)
C = $400 + $125p
Total cost when 0 phones are made = $400 + $125(0) = $400
Total cost when 1 phone are made = $400 + $125(1) = $525
Total cost when 2 phones are made = $400 + $125(2) = $650
Total cost when 3 phones are made = $400 + $125(3) = $775
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Identify the inequality or equality that describes the following situation. David drives over 9 miles per hour in the mall parking lot.
Step 1
Given; Identify the inequality or equality that describes the following situation. David drives over 9 miles per hour in the mall parking lot.
Step 2
Let x represent miles
y represents hours
Thus the inequality will be;
[tex]speed=\frac{distance}{time}[/tex][tex]\begin{gathered} Speed\text{ is over }9mph \\ This\text{ means David drives more than 9 miles per hour} \\ speed>9mph \end{gathered}[/tex]Answer; The required inequality is > or greater than because he drives over 9mph which means > 9mph
[tex]The\text{ required inequality is }>[/tex]If Mary fails her classes then she cannot graduate
in one year, a town recorded a total of 79 days it did not rain, how many days did it rain
Answer:
286
Step-by-step explanation:
there are 365 in a year
365-79
286
What will be the length of the railing from point A to point B? Show or explain how you got your answer.
To know the length of the railing from point A to point B you can use Pythagoras Theorem.
You draw a right triangle:
You use the given information to know the measure of the legs in the triangle:
You can see that the value of x is the height of 5 steps: 5(7.5 in).
Then:
[tex]x=5(7.5)=37.5in[/tex][tex]x=y=37.5in[/tex][tex]Z=2y=2(37.5in)=75in[/tex]The B is equal to the lenght of 10 steps: 10(9.5in):
Then:
[tex]B=10(9.5in)=95in[/tex]You have the next triangle:
You use the Pythagoras Theorem to find the h:
[tex]h=\sqrt[]{Z^2+B^2}[/tex][tex]h=\sqrt[]{75^2+95^2}[/tex][tex]h=\sqrt[]{14650}[/tex][tex]h=5\sqrt[]{586}\approx121.03in[/tex]The length of the railing from point A to point B is 121.03inAn object moves according to a law of motion, where, its position is described by the following function, s = f(t) = t^4 - 4t + 1. The time t is measured in seconds and s in meter.a. Sketch the velocity graph and determine when is the object moving in the positivedirection.b. Draw a diagram of the motion of the object and determine the total distancetraveled during the first 6 seconds.
SOLUTION
(a) The function given is the distance graph. The velocity fuction is the derivative of the distance function. This becomes
[tex]\begin{gathered} f(t)=t^4-4t+1 \\ f^{\prime}(t)=4t^3-4 \\ v=4t^3-4 \end{gathered}[/tex]the graph is shown below
From the velocity graph above, the function is moving in a positive direction from 1 second and beyond
(b) The diagram of motion of the object is shown in the distance graph below
The total distance travelled is the integral of the velocity function from 0 to 6 as shown below
[tex]\begin{gathered} \int_0^64x^3-4 \\ =[\frac{4x^4}{4}-4x]_0^6 \\ =[x^4-4x]_0^6=6^4-4(6)-(0^4-4(0)) \\ =1296-24-0 \\ =1272 \end{gathered}[/tex]Hence the answer is 1272 m
if Robbie can do 35 Jumping Jacks in 60 seconds how many seconds would it take him to do 14 jumping jacks
Based on the number of jumping jacks that Robbie can do in 60 seconds, the number of seconds it will take to do 14 jumping jacks is 24 seconds
How to find the number of seconds?To find the number of seconds that it takes Robbie to do 14 jumping jacks, find the number of seconds it takes to do a single jumping jack.
The number of seconds to do a single jumping jack is:
= 60 / 35
= 1.71 seconds
If 14 jumping jacks are to be done then the number of seconds would be:
= 1.71 x 14
= 24 seconds
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