Adam earned approximately 12.48% interest on his savings account over 10 years.
To find the rate of interest (r) earned by Adam, we can use the formula for compound interest:
A = P * (1 + r[tex])^{t}[/tex]
where:
A = ending amount ($1649 in this case)
P = principal (initial amount) ($100 in this case)
r = interest rate (what we want to find)
t = time (in years) (10 years in this case)
We know the values of A, P, and t, so we can plug them into the formula and solve for r:
1649 = 100 * (1 + r)¹⁰
Divide both sides of the equation by 100:
16.49 = (1 + r)¹⁰
Now, let's isolate (1 + r) by taking the 10th root of both sides:
(1 + r) = √(16.49)
(1 + r) ≈ 1.12479
Now, subtract 1 from both sides to find the value of r:
r ≈ 1.12479 - 1
r ≈ 0.12479
Finally, convert the decimal to a percentage to get the interest rate:
r ≈ 0.12479 * 100
r ≈ 12.48%
So, Adam earned approximately 12.48% interest on his savings account over 10 years.
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Carly withdraws $18 from her bank account which number line represents this amount ?
Answer:
it would be D
Step-by-step explanation:
Answer:
The number line D)
Step-by-step explanation:
Carly withdraws $18 from her bank account.
We assume that Carly has $x in her account. She withdraws $18 from her bank account.
So we have to subtract $18 from $x amount.
Which is $x - 18.
So we are subtracting $18 from her account.
It should be represented by an integer -18.
Now we have to identify the which number line represents -18.
It is D)
What is the volume of the composite figure?
cubic inches
12 in
4 in.
3 in
7 in.
Answer:
Where is the figure????
Step-by-step explanation:
What is the EQUATION of a HORIZONTAL LINE passing through THE POINT (-7, 5)?
A.y = 5
B.y=-7
C.x = 5
D.x= -7
Answer:
A. y = 5Step-by-step explanation:
A horizontal line has an equation: y = a (a - any real number).
Each point on a horizontal line y = a, has coordinates (x, a) (x - any real number).
We have the point (-7, 5) → y = 5
please could someone answer this
Answer:
29/12
Step-by-step explanation:
In an isosceles triangle, two sides are equal.
Therefore:
25/6+25/6+u = 10 3/4
50/6+u=43/4
u=43/4-50/6
u=43/4-25/3
u=129/12-100/12
u=29/12
If f(x) = x and g(x) = 2x + 7, what is
f[90X)] when g(x) = 11?
[tex]\bf \begin{cases} f(x) = x\\ g(x) = 2x+7 \end{cases}~\hspace{7em}g(x)=11\implies \stackrel{g(x)}{11}=2x+7 \\\\\\ 4=2x\implies \cfrac{4}{2}=x\implies \implies \boxed{2=x} \\\\[-0.35em] ~\dotfill\\\\ f[90x]\implies f\left[90\left( \boxed{2} \right)\right]\implies f(180)=\stackrel{x}{180}[/tex]
If h(x) = x – 7 and g(x) = x2, which expression is equivalent to (gon (5)?
(5 – 7)
O (5)2 – 7
O (5)?(5 – 7)
O (5 – 7)x2
Answer:
(5 - 7)²Step-by-step explanation:
[tex]h(x)=x-7,\ g(x)=x^2\\\\(g\circ h)(x)=g\bigg(h(x)\bigg)-\text{exchange x to x - 7 in}\ g(x):\\\\(g\circ h)(x)=(x-7)^2\\\\(g\circ h)(5)-\text{put x = 5 to the equation}\\\\(g\circ h)(5)=(5-7)^2[/tex]
A.) x+7/x-1
B.) x+1/x+7
C.) x-1/x+7
Answer:
C
Step-by-step explanation:
If there is an expression such as:
[tex]\frac{A*B}{A*C}[/tex]
we can cancel out A from top and bottom and that will leave us with [tex]\frac{B}{C}[/tex]
Note: Let A, B, C, be any algebraic expression
For the problem given, we can simply cut (x+1) from top and bottom by rules of algebra. So the remaining terms are:
[tex]\frac{(x-1)}{(x+7)}[/tex]
This is option C
Answer:
C)
Step-by-step explanation:
When you have a*b/c*a, a crosses out, simplifying to b/c:
(x+1)(x-1)/
(x+1)(x+7)
When "crossing out", you are really just simplifying it to 1/1:
1*(x-1)/
1*(x+7)
Which is the same as:
(x-1)/(x+7)
Therefore, C is the correct answer
Evaluate b2c-1 for b = -4 and c = 2.
When evaluating the expression [tex]b^2c - 1[/tex] for b = -4 and c = 2, we calculate b squared as 16, multiply by c to get 32, and subtract 1 to obtain the answer 31.
To evaluate the expression b2c - 1 for b = -4 and c = 2, we need to follow the order of operations, often referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, we calculate b², which is (-4)² = 16.
Next, we multiply this result by c, which gives us 16 * 2 = 32.
Finally, we subtract 1 from this product, resulting in 32 - 1 = 31.
Therefore, the evaluated expression [tex]b^2c - 1[/tex] is 31 when b = -4 and c = 2.
What is the area of a sector with a central angle of 5π6 radians and a radius of 5.6 ft? Use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
41.03 square feet
Step-by-step explanation:
The area of a sector is given by the formula:
[tex]A=\frac{1}{2}r^2\theta[/tex]
Where A is the area, r is the radius and [tex]\theta[/tex] is the angle in radians.
Given the values, we plug into the formula and solve:
[tex]A=\frac{1}{2}r^2\theta\\A=\frac{1}{2}(5.6)^2(\frac{5\pi}{6})\\A=41.03[/tex]
Which graph is a function of X? Explanation, please?
Answer:
V looking graph
(absolute value function)
Step-by-step explanation:
We are looking for a relation that passes the vertical line test.
Basically if you can play a vertical line on your graph and it touches more than once on that vertical line (your graph) then it isn't a function.
The only one that is a function here is the V looking graph.
The graph in the shape of a V (absolute value function)
We want a partnership that can withstand the vertical line test.Fundamentally, Whenever you really can play a vertical line in the graphs so it touches the vertical line (your graphs) more than once, it isn't a function.The only one that is a function here is the V-shaped graph.Learn more:
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Simplify the expression.
the quantity x to the one fifteenth power end quantity to the power of 5
Answer:
[tex]\sqrt[3]{x}[/tex]
Step-by-step explanation:
we have
[tex](x^{\frac{1}{15}})^{5}[/tex]
Simplify
Multiply the exponents
[tex](x^{\frac{1}{15}})^{5}=x^{\frac{1}{15}*5}=x^{\frac{5}{15}}=x^{\frac{1}{3}}=\sqrt[3]{x}[/tex]
Answer:
[tex]\sqrt[3]{x}[/tex].
Step-by-step explanation:
We have been given an expression [tex](x^{\frac{1}{15}})^5[/tex]. We are asked to simplify our given expression.
We will use power rule of exponents [tex](a^b)^c=a^{b\cdot c}[/tex] to simplify our given expression as:
[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{15}\times 5}[/tex]
[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{3}\times 1}[/tex]
[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{3}}[/tex]
Using fractional exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex], we can write our expression as:
[tex](x^{\frac{1}{15}})^5=\sqrt[3]{x}[/tex]
Therefore, the simplified form of our given expression would be [tex]\sqrt[3]{x}[/tex].
Find the equation of a circle with its center at (2,7) and a radius of 5.
Final answer:
The equation of a circle with center (2,7) and a radius of 5 is (x - 2)² + (y - 7)² = 25.
Explanation:
To find the equation of a circle with its center at (2,7) and a radius of 5, we use the standard form of the equation for a circle which is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.
Plugging in the given values for our circle we have:
(x - 2)² + (y - 7)² = 5²
Expanding the right side of the equation gives us:
(x - 2)² + (y - 7)² = 25
This is the desired equation of the circle. It represents a circle with a radius of 5, centered at the point (2,7).
find the values of angles x, y, and z.
Answer:
x = 80, y = 140 and z = 20
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles in the triangle with x and equate to 180
x + 60 + 40 = 180
x + 100 = 180 ( subtract 100 from both sides )
x = 80
40° and y form a straight angle and are supplementary, hence
40 + y = 180 ( subtract 40 from both sides )
y = 140
Sum the 3 angles in the triangle with z and equate to 180
z + y + 20 = 180, that is
z + 140 + 20 = 180
z + 160 = 180 ( subtract 160 from both sides )
z = 20
The first few steps in solving the quadratic equation 8x2 + 80x = −5 by completing the square are shown.
8x2 + 80x = −5
8(x2 + 10x) = −5
8(x2 + 10x + 25) = −5 + ______
Which number is missing in the last step?
Answer:
200
Step-by-step explanation:
8x^2 + 80x = −5
Factor out an 8
8(x^2 + 10x) = −5
Take the coefficient of the x term, divide by 2 and then square it
10/2 = 5, 5^2=25
Remember we have the 8 outside, so we are multiplying by 8
8*25 =200
Add 200 to each side
8(x^2 + 10x + 25) = −5 + 200
Answer:
Missing number is 200.
Step-by-step explanation:
In the completing the square method we follow the following steps,
Step 1 : Move constant term to the right side,
Step 2 : Make 1 as the coefficient of [tex]x^2[/tex]
Step 3 : Add square of the half of the coefficient of x in the left side and balance the equation,
Here, the given equation,
[tex]8x^2+ 80x = -5[/tex]
[tex]8(x^2 + 10x) = -5[/tex]
∵ coefficient of x = 10,
Half of 10 = 5,
Square of 5 = 25,
Thus, we need 25 inside the bracket in left side,
For this, add 200 on both side,
[tex]8(x^2 + 10x+25) = -5+200[/tex]
Hence, missing number in the last step is 200.
Order the numbers from least to greatest.
Answer:
3 1/2 ; 3 19/20 ; 3 39/40
Step-by-step explanation:
Find common denominators. Change all mixed fraction to improper fractions before finding common denominators.
3 1/2 = 6/2 + 1/2 = 7/2
3 19/20 = 60/20 + 19/20 = 79/20
3 39/40 = 120/40 + 39/40 = 159/40
Find the common denominators. The smallest common denominators is 40. Remember that what you do to the denominator you do to the numerator:
3 1/2 = (7/2)(20/20) = 140/40
3 19/20 = (79/20)(2/2) = 158/40
3 39/40 = (159/40) = 159/40
Least to Greatest:
3 1/2 ; 3 19/20 ; 3 39/40
~
You manage inventory for Swim Chem, a large distributor of chemicals for indoor and outdoor pool companies. Your division sold 2.4 tone of chlorine on Monday, 4.4 on Tuesday, 1.8 on Wednesday, and 2.8 on Thursday. If last week's sales totaled 14.4 tons, how much chlorine sold on Friday?
Answer:
[tex]\boxed{\text{3.0 T}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}M + T + W + Th + F & = & \text{Total}\\2.4 + 4.4 + 1.8 + 2.8 + F & = & 14.4\\11.4 + F & = & 14.4\\F & = & 3.0\\\end{array}\\\text{Friday's sales of chlorine were }\boxed{\textbf{3.0 T}}[/tex]
Answer: There are 3 tons of chlorine sold on Friday.
Step-by-step explanation:
Since we have given that
Number of tone of chlorine on Monday = 2.4
Number of tone of chlorine on Tuesday = 4.4
Number of tone of chlorine on Wednesday = 1.8
Number of tone of chlorine on Thursday = 2.8
Total number of week's sales = 14.4 tons
So, we need to find the number of tone of chlorine on Friday.
According to question we get that
[tex]14.4=2.4+4.4+1.8+2.8+x\\\\14.4=11.4+x\\\\x=14.4-11.4\\\\x=3[/tex]
Hence, there are 3 tons of chlorine sold on Friday.
Which shows a reasonable estimation for 124% of 42 using the distributive property?
Answer:
B 48
Step-by-step explanation:
it is b I know because I got it correct
Answer:
Its b
Step-by-step explanation:
You have to estimate the numbers so b is the best answer
Find the distance CA
C' ( 0, 3)
A' ( 2 , 1)
C'A' = CA
C'A' = √(2^2 + 2^2) = √8 = 2√2
C'A' = CA = 2√2
The distance between the points (2, 1) and (-2, 2) is √17, which is approximately 4.123 units.
We have,
The coordinates of point A =(2, 1) and C = (-2, 2)
Now,
To find the distance between two points, (x₁, y₁) and (x₂, y₂), we can use the distance formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Given the points (2, 1) and (-2, 2), we can substitute the values into the formula:
Distance = √[(-2 - 2)² + (2 - 1)²]
Distance = √[(-4)² + 1²]
Distance = √[16 + 1]
Distance = √17
Therefore,
The distance between the points (2, 1) and (-2, 2) is √17, which is approximately 4.123 units.
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The volume of an object is equal to the ratio of its mass to density, V = . The mass of a spherical grape is 8.4 grams and its density is 2 grams per cubic centimeter.
What is the radius of the grape? Round to the nearest tenth of a centimeter.
Step-by-step explanation:
Mass = Volume x density
Mass = 8.4 gm
Density = 2.4 g/cc
Substituting
8.4 = Volume x 2.4
Volume = 3.5 cm³
[tex]\texttt{Volume of sphere =}\frac{4}{3}\pi r^3[/tex]
We need to find radius, r
Substituting volume value
[tex]\texttt{Volume of sphere =}\frac{4}{3}\pi r^3=3.5\\\\r^3=0.836\\\\r=0.941cm=1cm[/tex]
Radius of grape = 1 cm
To solve the problem we must know about volume.
The radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.
What is volume?
The volume can be defined as the space occupied by the three-dimensional object.
It is given by the ratio of mass(m) and density(ρ).
[tex]\text{Volume of the object} = \dfrac{m}{\rho}[/tex]
Given to us
Mass of the object, m = 8.4 grams
Density of the object, ρ = 2 gram/cm³
As it is already mentioned that the volume is equal to the ratio of its mass to density. therefore,
[tex]\text{Volume of the object} = \dfrac{m}{\rho}\\\\\text{Volume of the object} = \dfrac{8.4}{2}\\\\\text{Volume of the object} = 4.2\ cm^3[/tex]
Thus, the volume of the object is 4.2 cm³.
To find the radius of the sphere we will use the formula of the volume of the sphere.
[tex]\text{Volume of sphere} = \dfrac{4}{3}\pi r ^3[/tex]
Substitute the values,
[tex]4.2 = \dfrac{4}{3}\pi r ^3\\\\r = 1\rm\ cm[/tex]
Hence, the radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.
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What is the volume of a rectangular crate that has dimensions 9 inches by 9 inches by 1 feet? 1,458 in.3 121.5 in.3 1,012.5 in.3 36 in.3
Answer:
case 1) 972 in³
case 2) 1,458 in³
Step-by-step explanation:
Remember that
1 ft=12 in
case 1)
If the dimensions of the crate are
9 in x 9 in x 1 ft
Convert to inches
9 in x 9 in x 12 in
The volume is equal to
V=9*9*12=972 in³
case 2)
If the dimensions of the crate are
9 in x 9 in x 1 1/2 ft
Convert to inches
9 in x 9 in x (12*1.5) in
9 in x 9 in x 18 in
The volume is equal to
V=9*9*18=1,458 in³
Answer:
121.5
Step-by-step explanation:
9x9x1.5=121.5
Let R be the region bounded by y=x and y=x^2.
Find the area of R.
Find the volume of the solid that results when R is revolved about the x-axis(using the shell method).
Answer:
2pi/15
Step-by-step explanation:
The intersection of y=x and y=x^2 is (0,0) and (1,1)
Washer method
Prefered this method for this one since slices are perpendicular to axis of rotation
Integrate(Big circle - Small Circle)dx
Integrate(pi*(x)^2-pi*(x^2)^2)dx on x=0..1
Integrate(pi*x^2-pi*x^4)dx on x=0..1 is 2pi/15
Shells method
So I have to solve for x since I will be integrating with respect to y
The height of the the shell will be sqrt(y)-y
The radius will be y since that is the distance between axis of rotation in a point within the shell
Integrate(2*pi*r*h ) dy
Integrate(2*pi*(sqrt(y)-y)*y) dy on y=0..1 is 2pi/15
James calculated the height of a cylinder that has a volume of 324
below.
cubic inches and a radius of 12 inches. His work is shown
V=Bn
Step 1: 3245 - 12h
Step 2: 324 = 24 sh
324 24
Step 3: 245 245
Step 4: h-13.5
inches
What is the first error that James made when calculating the height of the cylinder?
In step 1, he substituted into the volume formula incorrectly.
In step 2, he calculated 122 incorrectly. It should be 144 rather than 24.
In step 4, the should have canceled, making the correct answer 13.5 cm.
James calculated the height of the cylinder correctly
Answer:
In step 1, he substituted into the volume formula incorrectly.
Step-by-step explanation:
James calculated the height of a cylinder that has a volume of 324 cubic inches.
radius = 12 inches.
The formula for volume is = [tex]\pi r^{2} h[/tex]
So, James calculated wrongly by using the wrong formula.
The step 1 is wrong.
Answer:
In step 1, he substituted into the volume formula incorrectly.
Step-by-step explanation:
Match each inequality to the number line that represents its solution
Answer:
Part 1) shaded area at left of x=8 (close circle) ---> [tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]
Part 2) shaded area at left of x=-5 (close circle) ---> [tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]
Part 3) shaded area at left of x=-6 (close circle) ---> [tex]\frac{3x}{2}+105 \leq 96[/tex]
Part 4) shaded area at left of x=7 (close circle) ---> [tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]
see the attached figure
Step-by-step explanation:
Part 1) we have
[tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]
Multiply by -10 both sides
[tex]x-2 \leq 6[/tex]
Adds 2 both sides
[tex]x \leq 6+2[/tex]
[tex]x \leq 8[/tex]
The solution is the interval -----> (-∞,8]
All real numbers less than or equal to 8
In a number line the solution is the shaded area at left of x=8 (close circle)
Part 2) we have
[tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]
Multiply by -6 both sides
[tex]100x+11 \leq -489[/tex]
Subtract 11 both sides
[tex]100x \leq -489-11[/tex]
[tex]100x \leq -500[/tex]
Divide by 100 both sides
[tex]x \leq -5[/tex]
The solution is the interval -----> (-∞,-5]
All real numbers less than or equal to -5
In a number line the solution is the shaded area at left of x=-5 (close circle)
Part 3) we have
[tex]\frac{3x}{2}+105 \leq 96[/tex]
Multiply by 2 both sides
[tex]3x+210 \leq 192[/tex]
Subtract 210 both sides
[tex]3x \leq 192-210[/tex]
[tex]3x \leq -18[/tex]
Divide by 3 both sides
[tex]x \leq -18/3[/tex]
[tex]x \leq -6[/tex]
The solution is the interval -----> (-∞,-6]
All real numbers less than or equal to -6
In a number line the solution is the shaded area at left of x=-6 (close circle)
Part 4) we have
[tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]
Multiply by -18 both sides
[tex]13x-10 \leq 81[/tex]
Adds 10 both sides
[tex]13x \leq 91[/tex]
Divide by 13 both sides
[tex]x \leq 91/13[/tex]
[tex]x \leq 7[/tex]
The solution is the interval -----> (-∞,7]
All real numbers less than or equal to 7
In a number line the solution is the shaded area at left of x=7 (close circle)
PLEASE HELP 12 POINTS
Answer:
5:5 (first box, pencils to pens)
7:3 (second box, coloured pencils to crayons)
The probability of picking a pen (1st box): 5/10
The probability of picking a crayon (2nd box): 3/10
Probability of picking both: 5/10*3/10 = 15/100
From a point P, two tangents PA and PB
are drawn to a circle with center 0. If OP is equal to diameter of the circle, show
that triangle APB is equilateral.
Answer:bsdaosdfhaodsifhaosdfaidfhaoif
have a nice time reading and understanding his:)
Step-by-step explanation:
considering APB as the triangle
AP is the tangent to the circle.
∴ OA ⊥ AP (Radius is perpendicular to the tangent at the point of contact)
⇒ ∠OAP = 90º
In Δ OAP,
sin ∠OPA = OA/OP = r/2r [Diameter of the circle]
∴ sin ∠OPA = 1/2 = sin 30º
⇒ ∠OPA = 30º
Similarly, it can he prayed that ∠OPB = 30
How, LAB = LOP + LOB = 30° + 30° = 60°
In APB,
PA = PB [lengths &tangents drawn from an external point to circle areequal]
⇒ ∠PAB = ∠PBA --- (1) [Equal sides have equal angles apposite to them]
∠PAB + ∠PBA + ∠APB = 180° [Angle sum property]
∠PAB + ∠PBA + ∠APB = 180° - 60° [Using (1)]
⇒ 2∠PAB = 120°
⇒ ∠PAB = 60°
From (1) and (2)
∠PAB = ∠PBA = ∠APB = 60°
APB is an equilateral triangle.
Can someone help me please
Answer:
Multiply [tex] \frac { 3 } { 4 } [/tex] by 8.
Step-by-step explanation:
We are given the following expression and we are to find its quotient:
[tex] \frac { 3 } { 4 } [/tex] ÷ [tex] \frac { 1 } { 8 } [/tex]
This can also be written as:
[tex]\frac{\frac{3}{4}}{\frac{1}{8} }[/tex]
Since the two fractions are being divided so to change this division sign into a multiplication sign, we will take the reciprocal of the fraction in the denominator and multiply 3/4 by 8.
[tex]\frac{3}{4} \times 8[/tex] = 6
For this case we must find the quotient of the following expression:
[tex]\frac {\frac {3} {4}} {\frac {1} {8}} =[/tex]
Applying double C we have:
[tex]\frac {3 * 8} {4 * 1} =\\\frac {24} {4}[/tex]
This is equivalent to the following expression:
[tex]\frac {3} {4} * 8 = \frac {24} {4}[/tex]
Answer:
Option B
Which of the following is an odd function
Given the functions
(a) f(x) = x³ + 5x² + x
(b) f(x) = x² + x
(c) f(x) = -x
Function (a)
f(-x) = (-x)³ + 5(-x)² + (-x)
= -x³ + 5x² - x
= -(x³ - 5x² + x)
The function is neither even nor odd.
Function (b)
f(-x) = (-x)² + (-x)
= -(-x² + x)
The function is neither even nor odd.
Function (c)
f(-x) = -(-x)
= x
= -f(x)
Because f(-x) = -f(x) the function is odd.
Answer: f(x) = -x is an odd function.
Nancy had 16 chocolate candies in a bag. Her mother put a handful of candies in the bag. When Nancy counts her chocolate candies, she discovers she now has 32 of them. Which of the following equations will help Nancy solve for the number of chocolate candies, c, that her mom put in the bag?
16c = 32
c − 16 = 32
16 + 32 = c
16 + c = 32
The correct equation representing the situation where Nancy's mother added candies to the 16 candies already in the bag is 16 + c = 32. Subtracting 16 from both sides gives the result c = 16, which is the number of candies her mother added.
Explanation:The subject of this question is mathematics and it belongs to the middle school level. Nancy began with 16 candies and ended up with 32 candies after her mother added some. Nancy wants to find out how many candies her mother added.
To solve this problem, we need to use a simple addition equation. The equation that correctly represents the situation is 16 + c = 32. This equation says that Nancy's original amount of candies (16) plus the candies her mother added (c) equals the new total amount of candies (32).
To solve for c (the number of candies her mother added), we simply subtract 16 from both sides of the equation. Therefore, c = 32 - 16, which leads to c = 16, which is the number of candies her mom put in the bag.
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Final answer:
The correct equation for Nancy's chocolate candies is 16 + c = 32, solving for c reveals that 16 candies were added. Jenny initially had 14 chocolates before eating two and giving half of the remainder to Lisa.
Explanation:
The question asks to identify the correct equation to solve for the number of chocolate candies, c, that Nancy's mom put in the bag. Nancy originally had 16 chocolate candies, and her mother added some candies to the bag, increasing the total to 32 candies. The equation that represents this situation is 16 + c = 32. This equation can help Nancy find out how many candies her mother added to the bag.
To solve for c, we need to perform a subtraction operation:
32 - 16 = cThis calculation gives us the number of candies Nancy's mother added, which means c = 16 candies.
Jenny's Chocolate Question
If Jenny has some chocolates, eats two, and gives half of what is left to Lisa, resulting in Lisa having six chocolates, then we must work backward to find the initial amount. Since Lisa received half of the remainder, Jenny must have had 12 chocolates after eating two. This means Jenny started with 14 chocolates as:
14 - 2 = 12 (Jenny eats two)12 / 2 = 6 (Lisa gets half)The correct answer for Jenny's beginning number of chocolates is 14.
A daycare center charges a $75 enrollment fee plus $100 per week. Which of the following represents the cost of sending a child to daycare for 14 weeks?
Answer:
$1,475
Step-by-step explanation:
times 100 by 14 which is 1400
but then add 75 onto that
Answer:
$1475
Step-by-step explanation:
One week costs $100.
Note that:
The $75 enrollment fee is a one-time payment.
$100 per week is the amount that is paid per week, and can change depending on the amount of week they pay for.
In this case, the child would be there for 14 weeks. Set the equation. Let x = amount of weeks, and t = total cost:
100x + 75 = t
We know that the child will be there for 14 weeks, so plug in 14 for x.
(100)(14) + 75 = t
t = (100 * 14) + 75
Simplify. Remember to follow PEMDAS. Multiply first, then add:
t = (1400) + 75
t = 1475
The total cost for 14 weeks is $1475.
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Which situation is most likely to have a constant rate of change?
O
A. Distance a school bus travels compared with the number of stops
O
B. Number of trees in a park compared with the area of the park
C. Length of a bead necklace compared with the number of identical
beads
D. Number of runs scored in a baseball game compared with the
number of innings
Final answer:
The situation with a constant rate of change is the length of a bead necklace compared with the number of identical beads, as it represents a linear relationship with a constant slope.
Explanation:
The situation that is most likely to have a constant rate of change is option C, which describes the length of a bead necklace compared with the number of identical beads.
In this scenario, each bead added to the necklace increases its length by a consistent amount. This defines a linear relationship, where the rate of change, also known as the slope in a linear equation, remains constant.
For example, if one bead adds one centimeter to the necklace, then ten beads will add ten centimeters, indicating that the rate of change is one centimeter per bead.
This can be depicted graphically as a straight line when you plot the number of beads against the length of the necklace.