Answer:
21
Step-by-step explanation:
9 = 3*3
10 = 5*2
5*3 = 15
2*3 = 6
15 + 6 = 21
Susan bought a 1 kilogram bag of grapes. On the way home, she ate 125 grams of the grapes. How many grams of grapes does Susan have left? use math language and symbols to explain how you used the correct measurement units to solve the problem.
Susan has 875 grams of grapes left.
1. Susan bought a 1 kilogram bag of grapes, which is equivalent to 1000 grams (since there are 1000 grams in a kilogram).
2. Susan ate 125 grams of the grapes on her way home.
3. To find out how many grams of grapes Susan has left, we need to subtract the amount she ate from the initial weight of the bag. Therefore, we subtract 125 grams from 1000 grams.
1000 grams - 125 grams = 875 grams
4. Thus, Susan has 875 grams of grapes left.
measurement units:
In this problem, we used grams as the measurement unit. Grams are commonly used to measure the weight of small objects like grapes. Since the problem stated that Susan bought a 1 kilogram bag of grapes, it was necessary to convert the kilogram measurement to grams.
This conversion was done by multiplying the kilogram value by 1000 (1 kilogram = 1000 grams). By using the correct measurement units, we were able to accurately calculate the amount of grapes Susan had left after eating a portion.
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please help me so love this problem?
Answer:
12.7 ==> distance of RS
24.2 ==> distance of RT
Step-by-step explanation:
Distance is always positive. So if you get a negative value, take the absolute value of the negative number:
For example, between point R and S:
-17.2 - (-4.5) =
-17.2 + 4.5 = ==> subtracting a negative number is equivalent to adding a
positive number
-(17.2 - 4.5) = -12.7
-12.7 ==> |-12.7| = 12.7 ==> distance of RS
For RT:
-17.2 - 7 =
-(17.2 + 7) = -24.2
-24.2 ==> |-24.2| = 24.2 ==> distance of RT
Solve
a cylinder of radius r cm and height h cm has a curved surface area A cm\( {}^{2} \), where\(A = 2\pi rh.\)
a) obtain a formula for h
b) find the value of h when A = 93 ,R = 2.5 and \(\pi\)= 3.1
Answer:
(a) h = A/2πr
(b) 360.375
Step-by-step explanation:
(a) divide both sides by 2πr
h = A/2πr
(b) h= 93 / 2*3.1*2.5
= 360.375
1. 9x = 45 need to apply the 2. p + 44 = 126 3. - 12 =b-18 i need to apply the property of division property of equality subtraction I p=82
b=6, x=5
Explanation
\(-12=b-18\)Step 1
action: add 18 in both sides
property: Additive property: When a number is added or subtracted from both sides of the equality, the equality holds
then,add 18 in both sides
\(\begin{gathered} -12=b-18 \\ -12+18=b-18+18 \\ 6=b \\ b=6 \end{gathered}\)Step 2
\(9x=45\)Action:divide both sides by 9
The property for division : The property for division tells us that if we divide both sides of the equality by a real number (other than zero), we obtain another new valid equality.
\(\begin{gathered} 9x=45 \\ \frac{9x}{9}=\frac{45}{9} \\ x=5 \end{gathered}\)find the values of x where the graph of the function has a point of inflection given f(x)=x^4-x^3
f(x) has a point of inflection at x = 0 and x = 1/2.To find the values of x where the graph of the function\(f(x) = x^4 - x^3\) has a point of inflection, we need to find where the second derivative of the function changes sign from positive to negative or vice versa.
The first derivative of the function is:
\(f'(x) = 4x^3 - 3x^2\)
The second derivative of the function is:
\(f''(x) = 12x^2 - 6x\)
Setting f''(x) equal to zero and solving for x gives:
\(12x^2 - 6x = 0\)
6x(2x - 1) = 0
This equation has two solutions:
x = 0, or x = 1/2
To determine whether these values of x correspond to points of inflection, we need to look at the sign of the second derivative on either side of each value.
When x < 0, f''(x) is positive because both \(12x^2\) and -6x are positive. When 0 < x < 1/2, f''(x) is negative because \(12x^2\)is positive but -6x is negative. When x > 1/2, f''(x) is positive again because both \(12x^2\) and -6x are negative.
Therefore, f(x) has a point of inflection at x = 0 and x = 1/2.
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NEED HELP ASAP WILL GHVE BRAINLEST AND TONS OF POINTS
The value of the missing part of the triangle such as PR and ST = 8 and 5 respectively
How to calculate the value of the missing sides of the given triangle?Triangle PQS is congruent with triangle PRS
Therefore, PQ = PR
That is;
PQ = 8
PR = 2x
8 = 2x
X = 8/2 = 4
PR = 2(4) = 8
For ST;
Triangle VST = VUT
That is, TU = ST
ST = 5z
TU = 2z+3
5z = 2z+3
5z+2z = 3
z= 3/3 = 1
ST = 5(1) = 5
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pls help!! Which of the following are trinomials?
□ A. x² + 3
□ B. 6x² + ¹⁄y³
□ c. ¾/7y³ + 5y² + y
☐ D. x¹¹
□ E. x¹ + x² +1
☐ F. 8x
The algebraic expression known as a trinomial contains three terms then the trinomials exists 3y + 5y² + y and \($$x^4\) + x² + 1.
What is meant by trinomial?Three non-zero terms make up a trinomial, which is an algebraic expression. The algebraic expression known as a trinomial contains three terms. An mathematical equation called a trinomial has three terms with on-zero coefficients, each separated by a + or - sign. It is a trinomial if three monomials are divided by addition or subtraction.
When a polynomial has three terms, it is referred to as a trinomial. Its general expression is ax² + bx + c, where a and b are coefficients and c is a constant. In order to factor trinomials, you must follow these three easy steps: Calculate the values of b (middle term) and c. (last term).
A. 8x
Not a trinomial because, it contains only one term.
B. 3y +5y² + y
A trinomial because, it contains three terms.
C. 6x²
Not a trinomial because, it contains only one term.
D. \(x^{4}\) + x² +1
A trinomial because, it contains three terms.
E. x² + 3
Not a trinomial because, it contains two terms only.
F. x¹¹
Not a trinomial because, it contains only one term.
Therefore, the correct answer is
B. 3y + 5y² + y and D. \($$x^4\) + x² + 1
The complete question is:
Which of the following are trinomials?
A. 8x
B. 3y + 5y² + y
C. 6x²
D. \($$x^4\) + x² + 1
E. x² + 3
F. \($$x^{11\)
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find the sum of the smallest 7- digit number and largest 4-digit number
1009999
Hope it helps you...
anyone wanna help me with this??
Answer:
1.c
2.b
3. c
4.d
Step-by-step explanation:
leave an brainlest!
letter H represent marks height in inches Suzanne is 7 in shorter than Mark write an algebraic expression that represents Susan's height in inches
Answer:
H-7=Suzanne
Step-by-step explanation:
Mark's height is H, if Suzanne is 7 less than Mark, that means Suzanne is H-7
is anybody available to help pls?
Answer:
5ft
Step-by-step explanation:
ez asff
Can anyone help me please?
Answer:
a. 6 faces
b. rectangular prism
c 2x3x3
Step-by-step explanation:
Hope this helps if you need explanation just ask
Archaeology: Tree Rings. At Burnt Mesa Pueblo, the method of tree-ring dating gave the following years A.D. for an archaeological excavation site: 1189, 1271, 1267, 1272, 1268, 1316, 1275, 1317, 1275. Find a 90% confidence interval for the mean of all tree ring dates from this archeological site.
After answering the presented question, standard deviation t Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)
What is standard deviation?A statistic that expresses the variability or variation of a bunch of values is the standard deviation. A high standard deviation indicates that the values are more distributed, whereas a low standard deviation indicates that the numbers are closer to the set mean. The standard deviation is a measure of how far the data are from the mean (or ). When the standard deviation is small, the data tends to cluster around the mean; when it is great, the data is more spread. The standard deviation represents the average variability of the data collection. It displays the average deviation from the mean of each score.
Next, we need to find the t-value for a 90% confidence interval with 8 degrees of freedom (n-1):
t = t(0.05, 8) = 1.860
Now we can calculate the lower and upper bounds of the confidence interval:
Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)
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There are 12 paintings at an art show. Three of them are chosen randomly to
display in the gallery window. The order in which they are chosen does not
matter. How many ways are there to choose the paintings?
Answer:
220
Step-by-step explanation: a p e x
There are 220 ways to choose the paintings.
What is combination in mathematics?"Combination determines the number of possible arrangements in a collection of items where the order of the selection does not matter."
Formula for combination:\(^{n}C_r=\frac{n!}{r!(n-r)!}\)
For given example,
There are 12 paintings at an art show.
⇒ n = 12
Three of them are chosen randomly to display in the gallery window.
⇒ r = 3
So, using the formula for combination, the number of possible ways to choose the paintings would be,
\(\Rightarrow~ ^{n}C_r=\frac{n!}{r!(n-r)!}\\\\\Rightarrow~ ^{12}C_3=\frac{12!}{3!(12-3)!}\\\\\Rightarrow~ ^{12}C_3=\frac{12!}{3!\times 9!}\\\\\Rightarrow~^{12}C_3=220\)
Therefore, there are 220 ways to choose the paintings.
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w(n)= -n-2; Find w(10)
Answer: w(10) = -12
Step-by-step explanation:
w(n) = -n - 2; Find w(10)
w(10) = -(10) - 2
w(10) = -10 - 2
w(10) = -12
The area of a rectangular plot is 360 sq. m. Its length is given as 24 m. Find its breadth.
1
Cind the are of ther
Answer:
As an area can be any shape, there is no formula for finding length and breadth when given area But if you have a rectangle Area = length × breadth Which can be rearranged to give Bread
Step-by-step explanation:
Answer:
it is 15m wide.
Step-by-step explanation:
i dont know what "Cind the are of ther" means, but
15*24=360
10*20=240 + 5*24=120 = 15*24=360
The circle graph shows the result of a survey. In what way is this graph misleading? Explain.
Step-by-step explanation:
because the total sum of each percent is 90%
and it must be 100% as it is a full circle
F
G
H
J
If the diameter of a circle is 16 cm and the
intercepted arc length is 6m, what is the
measure of the central angle in radians?
3
8
3
7T
3
T
3²7
The measure of the central angle is 0.75 radians
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The length of an arc with an angle of Ф is given by:
Length of arc = (Ф/360) * (π * diameter)
The diameter is 16 cm and intercepted arc length is 6 cm, hence:
Length of arc = (Ф/360) * (π * diameter)
6 = (Ф/360) * (π * 16)
Ф = 42.97°
Ф = 42.97° * π/180 = 0.75 radian
The measure of the central angle is 0.75 radians
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Select the correct answer from each drop-down menu.
The total area of the three triangles is
square units.
The area of the figure is
square units.
The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
From the figure, the area of triangles can be calculated using the:
Area = (1/2)height×base length
Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)
Area of three triangle = 1/2(24×3) = 36 square units
Area of the figure = area of three triangle + area of the rectangle
= 36 + 6×4
= 60 square units
Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
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00:00Tyra has 12 cups of sugar. It r is the amount of sugar called for in one batch of cookies,the expression 12 tr can be used to find how many batches Tyra can make with the sugar she has.le ris ; cup, how many batches of cookies can Tyra make?Enter your answer in the box1.5batches
Tyra has 12 2/3 cups of sugar. If r is the amount of sugar called for in one batch of cookies,
the expression 12 2/3 ÷ r can be used to find how many batches Tyra can make with the sugar she has.
If r is 2/3 cup, how many batches of cookies can Tyra make?
__________________________________________
She has 12 2/3 cups
r (amount of sugar per batch)
Number of batches= cups of sugar/r
______________________________
Cups of sugar= 12 2/3 cups
r= 2/3 cup
12 2/3 ÷ 2 / 3
= (12*3 +2)/3 ÷ 2 / 3
= (36 +2)/3 ÷ 2 / 3
= (38)/3÷ 2 / 3
= 38/3 * 3/2
= 38*3 / 3*2
= 38/2
= 19
_____________________________
Answer
Tyra can make 19 batches of cookies if r is 2/3
Find the exact values of the numbers c that satisfy the conclusion of the Mean Value Theorem for the interval [−2, 2]. (Enter your answers as a comma-separated list.)
Answer:
The answer is "\(\bold{c= \pm \frac{2}{\sqrt{3}}}\)"
Step-by-step explanation:
If the function is:
\(\to f'(x) = 3x^2-2 \\\\\to f'(c) = 3c^2-2\)
points are:
\(\to -2 \leq x \leq2\)
use the mean value theorem:
\(\to f'(c) = \frac{ f(b)- f(a)}{b-a}\)
\(= \frac{ f(2)- f(-2)}{2-(-2)}\\\\= \frac{4-(-4) }{4}\\\\= \frac{8}{4}\\\\= 2\)
\(\to 3c^2-2=2 \\\\\to 3c^2=4 \\\\\to c^2=\frac{4}{3} \\\\c= \pm \frac{2}{\sqrt{3}}\)
5 1/2 + 3/4 Give your answer in its simplest form.
Answer:
5 1/2 + 3/4
11/2 + 3/4
22+3/4
25/4
=6 1/4
Which polynomial is prime?
O 3x³ + 3x² - 2x - 2
O 3x³ − 2x² + 3x − 4
-
O
4x³ + 2x² + 6x + 3
O
4x³+4x²-3x - 3
Answer:
B
Step-by-step explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
--------------------------------------------------
3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
----------------------------------------------------
4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
-------------------------------------------------
4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
--------------------------------------------------
the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4
unction g is a transformation of the parent tangent function such that
. Which graph represents function g?
A.
The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.
B.
The trigonometric functions intercept the x-axis at minus 4.2, minus 1.1, 2, and 5 units also pass parallel to the g of the x-axis.
C.
The trigonometric functions intercept the x-axis at minus 3.5, minus 0.2, and 3 units also pass parallel to the g of the x-axis.
D.
The trigonometric functions intercept the x-axis at minus 5, minus 2, 1, and 4.2 units also pass parallel to the g of the x-axis.
Answer:
A.
The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.
m ∠ � = ( � + 21 ) ∘ ∠A=(x+21) ∘ and m ∠ � = ( 4 � − 30 ) ∘ ∠B=(4x−30) ∘ , then find the measure of ∠ � ∠B.
The measure of angle B is given as follows:
m < B = 49.2º.
What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
The measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.As the angles are complementary, the value of x is obtained as follows:
x + 21 + 4x - 30 = 90
5x - 9 = 90
5x = 99
x = 19.8.
Hence the measure of angle B is obtained as follows:
m < B = 4 x 19.8 - 30
m < B = 49.2º.
Missing InformationThe measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.The angles are complementary, and it asks for the measure of angle B.
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which equation models the same quadratic relationship as function f? f(x)=x^2+12x+4 a) y=(x-6)^2+40 b) y=(x+6)^2-32 c) y=(x-6)^2-32 d) y=(x+6)^2+40
9514 1404 393
Answer:
b) y=(x+6)^2-32
Step-by-step explanation:
Add and subtract the square of half the x-coefficient to put into vertex form.
f(x) = x^2 +12x +4 . . . . . given
y = x^2 +12x +36 +4 -36 . . . . add and subtract (12/2)^2 = 36
y = (x +6)^2 -32 . . . . . . . . . . . write in vertex form
Answer:
B. Y=(x+6)²-32Step-by-step explanation:
hope it helps
(question 15) Find the derivative of the function
using logarithmic differentiation.
Answer:
\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)
Step-by-step explanation:
Replace f(x) with y in the given function:
\(y=(x+2)^x\)
Take natural logs of both sides of the equation:
\(\ln y=\ln (x+2)^x\)
\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)
\(\ln y=x\ln (x+2)\)
Differentiate using implicit differentiation.
Place d/dx in front of each term of the equation:
\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)
First, use the chain rule to differentiate terms in y only.
In practice, this means differentiate with respect to y, and place dy/dx at the end:
\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)
Now use the product rule to differentiate the terms in x (the right side of the equation).
\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)
\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)
\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)
Therefore:
\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)
Multiply both sides of the equation by y:
\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)
Substitute back in the expression for y:
\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)
Therefore, the differentiated function is:
\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)
\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)
What is the meaning of "each partition P of X defines an equivalence relation on X"?
The statement indicates that when a set X is partitioned, each partition forms an parity relation by grouping together rudiments that are considered original within each subset, thereby creating distinct and non-overlapping subsets within the original setX.
The statement" each partition P of X defines an parity relation on X" means that when a set X is divided into non-overlapping subsets or partitions, each partition creates an parity relation on the original set X.
An parity relation is a relation that satisfies three parcels reflexivity, harmony, and transitivity. In the environment of partitions, when a set X is divided into subsets, each partition forms an parity relation by grouping together rudiments that partake a common characteristic or property.
Within each partition, the rudiments are considered original or affiliated to each other, and they're distinct from rudiments in other partitions. The meaning of" each partition P of X" refers to every possible way of dividing the set X intonon-overlapping subsets.
It implies that different partitions may live grounded on different criteria or conditions for grouping rudiments.
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how would I find the equation of this graph
Answer:
y = sec(x-2) - 1
Step-by-step explanation:
We can determine the graph is of a secant by the repeating parabolas. From there, graph sec(x) and add the transformations necessary to replicate the graph.
The perimeter
particular rectangle is
36 centimeters. The longer sides of the rectangle are
cach 2 centimeters longer than each of the shorter sides
of the rectangle. What is the length, in centimeters, of
one of the longer sides of this rectangle"?
Answer:
Long side of the rectangle: 11cm
Shorter side of the rectangle: 7cm
Step-by-step explanation:
36cm divided by 4 = 9
9-2=7
take that two and add it to the other two nines
9+2=11
The required length of the longer sides of rectangle is 10cm.
The perimeter of the rectangle is 36 centimeters,
length = 2+ width
rectangle is four sided polygon whose opposites sides are equal and has angle of 90° between its sides.
Perimeter = 2 length x 2 width
36 = 2(2+width) x 2width
36= 4 (1+width)
width = 8
length= 2+width
length = 2+ 8
length = 10 centimeters
Thus, The required length of the longer sides of rectangle is 10cm.
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