The instantaneous rate of change refers to the derivative of f(x), so let's find that first, following the power rule, we have.
[tex]f^{\prime}(x)=1\cdot5x^{1-1}=5x^0=5\cdot1=5[/tex]As you can observe, the instantaneous rate of change is a constant, which means we don't have to evaluate it at x=9.
Therefore, the instantaneous rate of change is f'(x) = 5.How would you
describe the
following events, of
randomly rolling 2
dice and having a
sum that is EVEN OR
GREATER THAN 9?
The probability of the given event randomly rolling two dice and having a sum that is even or greater than 9 is 2/3.
As given,
Let us assume X is the event of the sum of two dice is even
Therefore
P(X) = The probability of having an even sum of two dice
Since all events are given in the question image, then
n(S) = Sample space = 36
X = {(1,1) , (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)}
n(X) = 18
Since
P(X) = n(A)/n(S)
P(X) = 18/36
P(X) = 1/2
Let us assume Y is the event of the sum of two dice is greater than 9, then
Y = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}
n(Y) 6
P(Y) = n(Y)/n(S)
P(Y) = 6/36
P(Y) = 1/6
P(X∪Y) = P(A) + P(B)
= 1/2 + 1/6
= 4/6
= 2/3
Therefore, probability of the given event randomly rolling two dice and having a sum that is even or greater than 9 is 2/3.
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True or False for each one613 rounded to the nearest ten is 610.1,970 rounded to the nearest hundred is 1,900.54,318 rounded to the nearest thousand is 54,000.476,022 rounded to the nearest ten thousand is 470,000.
To round a number to a specific place, look at the number to the right of that place. If the number is less than 5, round down. If it is greater than or equal to 5, round up.
Question 1: 613 rounded to the nearest ten is 610.
The tens digit in 613 is 1. To the right of 1 is 3. Therefore, the approximation of 613 is:
[tex]613\approx610[/tex]THIS STATEMENT IS TRUE.
Question 2: 1,970 rounded to the nearest hundred is 1,900.
The hundreds digit in 1,970 is 9. To the right of 9 is 7. This means that we will round up by adding 1 to 9. Therefore, the approximation will be:
[tex]1970\approx1900+100=2000[/tex]THIS STATEMENT IS FALSE.
Question 3: 54,318 rounded to the nearest thousand is 54,000.
The thousands digit is 4. To the right of 4 is 3. Therefore, the approximation is:
[tex]54318\approx54000[/tex]THIS STATEMENT IS TRUE.
Question 4: 476,022 rounded to the nearest ten thousand is 470,000.
The ten thousands digit is 7. To the right of 7 is 6. This means that we will round up. Therefore, the approximation is:
[tex]476022\approx470000+10000=480000[/tex]THIS STATEMENT IS FALSE.
The list price of a smartphone is $299. A local Samsung dealer receives a trade discount of 20% find the trade discount amount and the net price.
ANSWER
Discount amount = $59.80
Net price = $239.20
EXPLANATION
We are given that the price list of the smartphone at the store is $299.
The Samsung dealer receives a trade discount of 20%.
This means that 20% of the price was taken off for the dealer.
To find the discount amount, we need to find 20% of $299.
That is:
[tex]\frac{20}{100}\cdot\text{ 299 = }4=\text{ \$59.80}[/tex]That is the discount amount.
To find the net price, we simply need to deduct the discount amount from the list price.
That is:
Net price = $239.20
That is the net price.
escribe dos raciones q sean igual y explicalas
EXPLICACION.
Dos razones forman una proporcion cuando se da la siguiente condicion ;
el producto de sus extremos es igual al producto de sus medios.Veamos un ejemplo:
Un ejemplo de razones que se pueden hallar facilmente y saber si realmente es verdadera o exacta la proporcion es el siguiente ejemplo:
[tex]\begin{gathered} \frac{80}{4}=\frac{200}{10},\text{aqui debemos multiplicar en cruz} \\ entonces\text{ quedaria:} \\ 80\times10=200\times4 \\ \textcolor{#FF7968}{800=800;}\text{ } \\ \text{Como vemos el resultado es el mismo por lo tanto las dos razones } \\ \text{son iguales o verdadera.} \end{gathered}[/tex]IM DESPERATE I would like an explanation to go with the answer. THANK YOUOnly #5 and #6
Therefore the original price is $299
[tex]6)\text{ selling price = 152+152}\times\frac{50}{100}=152+76=228[/tex]the selling price is $228
QuestionThe unknown triangle ABC has angle A = 56° and sides a = 32 and c = 34. How many solutions are there for triangleABC? if there are infinitely many, enter oo.
The law of sines is a theorem for triangle which states that for a triangle with sides a,b,c and angle A,B,C
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]Where,
a=32
A=56
c=34
[tex]\begin{gathered} \frac{32}{\sin56}=\frac{b}{\sin B}=\frac{34}{\sin C} \\ \frac{32}{\sin56}=\frac{34}{\sin C} \\ \sin C=\frac{34\times\sin 56}{32} \\ \sin C=0.881 \end{gathered}[/tex][tex]\begin{gathered} \frac{b}{\sin B}=38.598 \\ b=38.598\sin B \\ \frac{b}{\sin B}=\frac{34}{\sin C} \\ \frac{38.598\sin B}{\sin B}=\frac{34}{0.811} \\ 38.598\ne41.92 \end{gathered}[/tex]For b and B is not full fill the condition of traiangle so zero triangle from ABC.
127x
10
0
6
4
--5-4-3 1₂
10
Mark this and return
169
909
4 5 6 x
Which statement is true regarding the functions on the
graph?
Of(-3)=g(-4)
Of(-4)= g(-3)
Of(-3)=g(-3)
Of(-4)= g(-4)
Answer:
NJ and the other day and t I don't know what to do it again and again and again and again and again and again and again and again and again and again and again and again and again I will be a good night my dear sister and her and I will have to go in
Select two values that are less than m.
+
Answer:
A, D are correct.
Step-by-step explanation:
M=1.2 according to the image so anything below that is the answer.
complete the table below to find the solutions to the linear equation y= 5x-5
Answer:
x y (x, y)
0 -5 (0, -5)
2 5 (2, 5)
1 0 (1, 0)
Explanation:
To fill a table, we need to give values to the variable x and then calculate the values of y.
So, if x = 0, then y is equal to:
y = 5x - 5
y = 5(0) - 5
y = 0 - 5
y = -5
If x = 2, then y is equal to:
y = 5x - 5
y = 5(2) - 5
y = 10 - 5
y = 5
If x = 1, then y is equal to:
y = 5x - 5
y = 5(1) - 5
y = 5 - 5
y = 0
Therefore, the complete table would be:
x y (x, y)
0 -5 (0, -5)
2 5 (2, 5)
1 0 (1, 0)
A bag contains 5kg of rice 1g is taken for cooking.what is the ratio of the amount taken out to the original quantity
1g of rice is taken from a bag containing 5kg of rice for cooking. The ratio of the amount taken out to the original amount is 5:1.
What is meant by ratio?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion exists in an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls) One-quarter are boys and three-quarters are girls. A ratio shows the number of terms one numeral contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
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if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<17
Since angle 16 measures 139 degrees and is a supplementary angle with angle 17, we have the following equation:
[tex]139+\measuredangle17=180[/tex]solving for angle 17, we get:
[tex]\begin{gathered} 139+\measuredangle17=180 \\ \Rightarrow\measuredangle17=180-139=41 \\ \measuredangle17=41\degree \end{gathered}[/tex]therefore, the measure of angle 17 is 41 degrees
Quiana took out a loan to pay for a new car. Initially, she owed the lender $15,234.68. She has repaid $247.43 of the loan each month for the past 5 months. What is the net change to the loan from Quiana’s perspective over the past 5 months?
Complete the steps below to help Quiana calculate the loan amount that she’s repaid to the lender.
Answer:
13,325
Step-by-step explanation:
247.43 x 5
13,535
Complete each proof using the properties of equality. ALL POWS W
Type the properties how they are listed above.
18; Prove: = 10
Ensuring that each person has an equal chance to maximize their potential is what equality is all about.
How is the equality property demonstrated?Proof: Given that A = B and B = C, we can infer that A = C according to the transitive principle. A = C and C = D are both true if we also know that C = D. We shall ultimately get at A = D after one more transitive property application.
The symmetrical attribute of equality
This fact, which states that if
18 + 10 =28,
then
28 = 10 + 18,
Serves as an example of the equality's symmetric property. The symmetric property of equality in mathematics is actually fairly straightforward. According to this principle, if a = b, then b =a.
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1.64÷3??? -------------------
Answer:
0.54666666666
Step-by-step explanation:
i don't know why but that is the answer
If A=(2,-3,-4) and B(6,7,-4), find ||AB||. Round to 3 decimal places.Type your answer...
The rule we will use is
[tex]\parallel AB\parallel=\sqrt[]{(x2-x1)^2+(y2-y1)^2+(z2-z1)^2}[/tex]x1 = 2 and x2 = 6
y1 = -3 and y2 = 7
z1 = -4 and z2 = -4
[tex]\parallel AB\parallel=\sqrt[]{(6-2)^2+(7--3)^2+(-4--4)^2}[/tex]Now we will find the answer in decimal using the calculator
The answer is 10.77032961
Round it to 3 decimal places, then
[tex]\parallel AB\parallel=10.770[/tex]In slurfball, a fizzy is worth 2 points and a globbo is worth 5 points. K and W recently played for the surfball game. During the game, K scored eight more Fizzles then the W, but scored five fewer flobbos then the W, together the two teams scored 93 points total. What was the final score?
Using mathematical operations of addition, multiplication, division, and subtraction, the final score was:
K = 42 points
W = 51 points.
What are mathematical operations?
The basic mathematical operations for getting mathematical results from numbers, values, and variables include addition, multiplication, division, and subtraction.
In this situation, we apply these four basic mathematical operations.
Fizzy = 2 points
X = 5 points
Total scores = 93 points
The points in 8 Fizzy = 16 points (8 x 2)
The points in 5 X s = 25 points (5 x 5)
The equation showing the total scores of K = total scores + 16 - 25
= (93 + 16 - 25)/2
= 42 points
The equation showing the total scores of W = total scores - 16 + 25
= (93 - 16 + 25)/2
= 51 points
Hence, Final scores are K = 42 and W = 51.
Thus, applying mathematical operations, the final score shows that K scored 42 points while W scored 51 points, totaling 93 points for the two teams.
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I need help finding the answer.A parallelogram must be a rectangle if it's diagonals:A. bisect the angles in the parallelogramB. are congruentC. are perpendicular to each otherD. bisect each other
Given:
A parallelogram must be a rectangle.
If the diagonals are congruent then the parallelogram must be a rectangle.
Option B is the final answer.
3 cm 00 What is the length of AC? A 1.5 cm C 6 cm B 3 cm D 9 cm is Which statement MUST be true? A AD BC В AD - BD CBD - AD D CDAD
The length of AC must be 3 cm letter B
Second question
Both B and C are correct.
Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)
Vertex:
(−3, −11);
point:
(0, 7)
The standard form of the quadratic function is- y = 2x² + 12x + 7
Here, we are given-
Vertex coordinate = (-3, -11)
Point on the graph = (0, 7)
The vertex form of a quadratic equation is given as-
y = a(x - h)² + k
Where h, k are the coordinates of the vertex.
a is the letter in general form of quadratic equation which is-
y = ax² + bx + c
Thus, here, h = -3, k = -11, x = 0 and y = 7
Substituting these values in the vertex form we get-
7 = a(0 - (-3))² - 11
⇒ 7 + 11 = 9a
9a = 18
a = 18/9
a = 2
Thus, the standard form of the quadratic equation can be calculated as-
y = 2(x - (-3))² - 11
y = 2x² + 12x + 18 - 11
y = 2x² + 12x + 7
Thus, the standard form of the quadratic function is- y = 2x² + 12x + 7
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help me please
thank you
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
(PLEASE ANSWER) Complete the proof that the diagonals of parallelogram ABCD bisect each other.
The missing statements and reasons in the proof are 5) Δ AEB ≅ Δ CED and Δ AED ≅ Δ CEB, 5) By ASA rule and 6) AE ≅ CE and DE ≅ EB
What is a parallelogram?A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
Given that, ABCD is a parallelogram, we need to prove that the diagonals of parallelogram ABCD bisect each other.
The proof is as follows,
Statement Reason
1) AB CD and AD BC Given
2) ∠ 1 = ∠ 3 When a transversal crosses
parallel lines, alternate interior
angles are congruent.
3) ∠ 2 = ∠ 4 When a transversal crosses
parallel lines, alternate interior
angles are congruent.
4) AB = CD Opposite sides of a
parallelogram are congruent.
5) Δ AEB ≅ Δ CED
and Δ AED ≅ Δ CEB By ASA rule
6) AE ≅ CE and DE ≅ EB Corresponding parts of
congruent triangles are congruent,
7) Point E bisects both AC and BD Definition of bisector
Hence, proved.
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Solve for V₂.
V2:
S=(v₁-v₂) w/5
The value is [tex]v_{2}=v_{1}-\frac{5s}{w}[/tex]
What is an equation?
a mathematical statement that shows that two expressions are equal is known as expression.
We are given an equation [tex]s=\frac{(v_{1}-v_{2} )w }{5}[/tex]
Multiplying both sides by 5 we get
[tex]5s=(v_{1}-v_{2})w[/tex]
Dividing both sides by w,
[tex]\frac{5s}{w}=v_{1}-v_{2}[/tex]
Rearranging the equation we get,
[tex]v_{2}=v_{1}-\frac{5s}{w}[/tex]
Therefore the value is [tex]v_{2}=v_{1}-\frac{5s}{w}[/tex]
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8. Let f(x) = 3x and g(x) = (x + 2)^2. Find the value of (g o f)(4).*A.54B.108C.196D.432
Answer
Option C is correct.
(g o f)(4) = 196
Step-by-step Explanation
f(x) = 3x
g(x) = (x + 2)²
We are then told to find
(g o f)(4)
We need to first interprete what (g o f) means
(g o f) refers to writing g(x) with f(x) replacing x. That is, f(x) replaces all the x that the function given by g(x) has.
(g o f) = g[f(x)]
g(x) = (x + 2)²
g[f(x)] = [f(x) + 2]²
Recall that f(x) = 3x
g[f(x)] = [3x + 2]²
We can then go further now to obtain (g o f)(4)
(g o f)(x) = g[f(x)] = [3x + 2]²
(g o f)(4) = [3(4) + 2]²
= [12 + 2]²
= 14²
= 196
Hence, option C is correct.
(g o f)(4) = 196
Hope this Helps!!!
Which of the following represents a compound?
H
H-3
H2O
O-16
Answer:
Step-by-step explanation:
Explain the meaning of the point (1,2.5) In terms of the situation
Given
The recipe for the smoothie is made up of 5 cups of strawberries and 2 cups of bananas.
For the point (1,2.5)
It means that from the graph showing a plot of the numbers of cups, with the number of strawberries cups on the y-axis and the number of banana cups on the x-axis, the 2.5 is for the number of cups for strawberries while 1 is the number of cups of banana.
We can also say that
For every 1 cup of banana, there should be 2.5 cups of strawberries.
6. Which inequality has the solution set shown in the graph below? cont OTTO -7 -6 -5 -4 -3-2-1-1 1 2 3 4 5 6 7 T
First we need write the equation of the line
we start from the general equation
[tex]y=mx+b[/tex]we need find m(slope) and b(cut point)
for the slope
we choose 2 points and find
(0,5)and(1,3)
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{3-5}{1-0} \\ m=-\frac{2}{1} \\ m=-2 \end{gathered}[/tex]the slope is -2
we can replace on the general equation with a point(0,5) and solve b
for b
[tex]\begin{gathered} y=(-2)x+b \\ 5=(-2)(0)+b \\ 5=0+b \\ b=5 \end{gathered}[/tex]replacing m and b, the final equation is
[tex]y=-2x+5[/tex]now, our inequality tells us that it takes into account the values below the line without taking the line (because it is dotted)
so we change = for <
the inequality is
[tex]y<-2x+5[/tex]Study Surface Area and Volume of Pyramid and Cone. How to find lateral area and total surface area of pyramid? please include one(1) problem per question with solutions.
Let's apply the formula for the lateral area and total surface area of a pyramid.
• Lateral Surface Area:
To find the lateral area of a pyramid, apply the formula:
[tex]A_l=\frac{1}{2}ps[/tex]Where:
p is the perimeter of the base
s is the slant height.
Example:
From the above square base pyramid, we have:
length of base, b = 4 cm
Slant height, s = 3 cm
Let's find the lateral area.
Since the base is a square, the perimeter will be:
p = 4 x 4 = 16 cm
Hence, to find the lateral area, we have:
[tex]\begin{gathered} A_l=\frac{1}{2}ps \\ \\ A_l=\frac{1}{2}\times16\times3 \\ \\ A_l=24\operatorname{cm}^2 \end{gathered}[/tex]Therefore, the lateral area of the square base pyramid above is 24 cm².
• Total surface area of a pyramid.
To find the total surface area of a pyramid, apply the formula:
[tex]A_s=\frac{1}{2}Ps+A[/tex]Where:
A is the area of the base
p is the perimeter of the base
s is the slant height.
Or we can simply say, the formula for total surface area is:
Total surface area = Lateral area + Area of base
Example:
Using the squarea base pyramid above, we have:
Area of base = 4 x 4 = 16 cm²
Lateral area = 24 cm²
Total surface area = 24 cm² + 16 cm² = 40 cm².
Most television show juice 13 minute of every hour for commercial leaving the remaining 47 minutes for the actual actual one popular television show wants to change the ratio of commercial time to show time to be 3 to 7 create two ratio tables one for normal ratio of commercials to programming and another one for the proposal ratio of commercial some programming use a ratio table to make a statement about which ratio with me and fewer commercials for viewers watch into our television
Answer: 39
Step-by-step explanation: 1889 - 1927 = 30
What is the first step in solving a quadratic equation of the form given below?
(ax + b)² = c
Answer:
take square root on both side
Step-by-step explanation:
How do I plot this linear inequalitie
Given the following inequality:
[tex]y\ge x-4[/tex]To plot the inequality, first we will plot the line y = x - 4
We will graph the line using the intercepts
When x = 0, y = -4
When y = 0, x = 4
So, the line passes through the points (4, 0) and (0, -4)
The graph of the line will be solid
Now, we will find the area that will be shaded to represent the answer.
Use the point (0, 0)
So, 0 ≥ 0 - 4
So, the point (0, 0) lying in the solution area.
the plot of the inequality will be as shown in the following figure:
When x = 0, y = -4
When y = 0, x = 4
So, the line passes through the points (ng the intercepts
When x = 0, y =
