Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total are 4.60. How many of each coin does he have.
Let x represent dimes (0.1), y represent nickels (0.5) and z represent quarter (0.25)
Hence:
0.1x + 0.05y + 0.25z = 4.6 (1)
Also:
x = 3y (2)
And:
z = y + 4 (3)
From the equations:
x = 18, y = 6, z = 10
Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Maria had a seven square-foot piece of construction paper. She used four square feet of the paper to make a large greeting card for a friend. Which operation would help to find the amount of paper she could use for another card? O division O addition subtraction multiplication
Answer:
subtraction
Step-by-step explanation:
If she had 7 sqft and used up 4 sqft, she no longer has that 4 sqft. It's used up, gone, taken away. We remove it from her total. That is "take away" this means subtraction.
7 - 4
= 3 she has 3sqft of construction paper left.
121 slabs . How many slabs will she need to lay in each row to make a square
She needs to lay 11 slabs on each row to make a square
How to determine the number of slabs in each row?The total number of slabs is given as:
Total = 121 slabs
Let this represent the area of the slab.
The area of a square is calculated as:
Area = Length^2
Substitute the known values in the above equation
Length^2 = 121
Take the square root of both sides
Length = 11
Hence, she needs to lay 11 slabs on each row to make a square
Read more about squares at:
https://brainly.com/question/24487155
#SPJ1
A freighter has to go around an oil spill in the Pacific Ocean. The captain sails due east for 30 miles. Then he turns the ship and heads due north for 14 miles. What is the distance and direction of the ship from its original point of course correction? Round each number to the nearest whole number.
The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.
Let x represent the distance travelled, hence:
x² = 14² + 30²
x = 33 miles
tanФ = 14/33
Ф = 23°
The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
please help with question
Applying precedence of operations, the result of the expression is of 161.
What is the precedence of operations?Power operations are done before multiplication/division, which are also done before addition/subtraction.
Operations inside brackets or parenthesis also take precedence.
In this problem, the operation is:
[3 x 2^5 + 13 x (-2)] + 7[8 - (4 - 9)]
First the power:
[3 x 32 + 13 x (-2)] + 7[8 - (4 - 9)]
Now the multiplications on the first bracket, and the subtraction on the second:
[96 - 26] + 7[8 - (-5)]
Then, applying the parenthesis to the negative number, we have that:
[96 - 26] + 7[8 - (-5)] = 70 + 7 x 13 = 161.
More can be learned about precedence of operations at https://brainly.com/question/550188
#SPJ1
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3 \times 2^5 + 13(-2)] + 7[8 - (4 - 9)]}[/tex]
[tex]\mathsf{= 3\times32 + 13\times -2 + 7[8 - (4 - 9)] }[/tex]
[tex]\mathsf{= 96 + 13\times -2 + 7(8 - (4 - 9))}[/tex]
[tex]\mathsf{= 96 - 26 + 7(8 - (4 - 9))}[/tex]
[tex]\mathsf{= 70 + 7(8 - (4 - 9))}[/tex]
[tex]\mathsf{= 70 + 7(8 - (-5))}[/tex]
[tex]\mathsf{= 70 + 7\times13}[/tex]
[tex]\mathsf{= 70 + 91}[/tex]
[tex]\mathsf{= 161}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{161}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer the following.
(a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation.
(b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.
Answer:
server timed out. unable to load your answer. please try again later
a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.
b. 1.1105 pounds is written in standard notation as 1.1105 pounds.
We have,
(a) To write the number 0.00000896 moles per liter in scientific notation, we move the decimal point to the right until there is one
non-zero digit to the left of the decimal point.
The number of decimal places we moved to the decimal point will be the exponent of 10 in the scientific notation.
So,
= 0.00000896
= 896/100000000
= 896 x 100/100 x [tex]10^{-8}[/tex]
= 896/100 x [tex]10^{-8 + 2}[/tex]
= 8.96 × [tex]10^{-6}[/tex]
(b)
To write the number 1.1105 pounds in standard notation, we simply write the number as it is, without any scientific notation or exponent.
1.1105 pounds is written in standard notation as 1.1105 pounds.
Thus,
a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.
b. 1.1105 pounds is written in standard notation as 1.1105 pounds.
Learn more about scientific notation here:
https://brainly.com/question/18073768P
#SPJ3
50 POINTS! Plot function h on the graph.
NO LINKS
See attachment for the graph of the piecewise function h(x)
How to plot the function?The function is given as:
h(x) = | -4, x < 3
| x + 5, x >= 3
The above function is a piecewise function.
It has 2 separate functions at two domains
This means that we plot the sub-functions in the piecewise function at their respective domain
See attachment for the graph of the piecewise function h(x)
Read more about piecewise function at:
https://brainly.com/question/27262465
#SPJ1
Use the method of equating coefficients to find the values of a, b, and c: (x+4)(ax2+bx+c)=−2x3−7x2+3x−4.
The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Given the polynomial:
-2x³ - 7x² + 3x - 4
Simplifying:
= -(2x² - x + 1)(x + 4)
Hence:
-2x³ - 7x² + 3x - 4 = (-2x² + x - 1)(x + 4)
(x + 4)(ax² + bx + c) = −2x³ − 7x² + 3x − 4
The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Can u guys please give me the correct answe
angle at y and w are equal
hence, 54°=w
54°+w+x =180°
x=180-(54°+54°)
x=72°
need heeeelp please
Answer:
7.61577310586
Step-by-step explanation:
Pythagoras Theorem 7 squared + 3 squared= 49+9=58
[tex]\sqrt{58}[/tex]
Show all work to write the expression in simplified rational exponent form:
[tex](\sqrt[4]{x^{2}+4 } )^{3}[/tex]
(Fourth root of x squared plus four, cubed)
Answer:
[tex]x^{\frac{1}{2} } + 48[/tex]
Step-by-step explanation:
This is hard to explain, but basically you use exponent rules to switch it to an exponent
[tex](\sqrt[4]{x^{2} +4} )^{3}[/tex]
It's easiest if you calculate [tex]4^{3}[/tex] first
4³ = 4 x 4 x 4 = 48
Then convert the root to a fraction exponent
[tex]\sqrt[4]{x^{2}} = x^{\frac{2}{4}} = x^{\frac{1}{2} }[/tex]
Combine them using addition, since addition was in the problem
[tex]x^{\frac{1}{2} } + 48[/tex]
I hope this helps!
Toenails grow at an average rate of about 0.05 mm per day, and the average toenail is about 3/4 inch long. About how many months does it take for a toenail to completely regenerate itself?
The number of months taken for the toenail to completely regenerate itself is 13 months
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
We have,
Toenail grows:
0.05 mm per day
0.05 mm = 1 day
[ 1 inch = 25.4 mm ]
So,
1 mm = 1/25.4 inch
0.05 x 1/25.4 inch = 1 day
0.0019 inch = 1 day
Divide both sides by 0.0019
1 inch = 1/0.0019 day
1 inch = 526.32 days
Multiply 3/4 on both sides.
3/4 inch = 3/4 x 526.32 days
3/4 inch = 395 days _____(1)
We can assume,
1 month = 30 days
Multiply 395/30 on both sides.
395/30 months = 395 days
13 months = 395 days _____(2)
From (1) and (2) we get,
3/4 inch = 13 months
Thus,
The number of months taken for the toenail to completely regenerate itself is 13 months.
Learn more about unit rates here:
https://brainly.com/question/11258929
#SPJ2
HELP ASAP WITH EXPLANATION: If f(x) + f(2 − x) = 4 for all x, find f(y − 2) + f(4 − y)
Answer:
f(y-2)+f(4-y)=4
Step-by-step explanation:
Assume (let) x=y-2
So: y=x+2
f(y-2)+f(4-y)=f(x)+f(-x+2)=f(x)+f(2-x)
The value of that expression is 4 from the given.
A 1L IV contains 60meq of kcal. The IV was discontinued after 400ml has infused. How much lvl did the patient receive
If a 1L IV contains 60meq of kcal and the IV was discontinued after 400ml has infused, then the amount of IV received by the patient is 24meq of kcal.
Calculation for the Amount of IV
It is given that,
1L IV contains 60meq of kcal
⇒ 1000 mL of IV contains 60meq of kcal
⇒ 1 mL of IV will contain 60 / 1000 meq of kcal
As per the question,
The amount of IV infused in the patient = 400 mL
⇒ The amount of IV received by the patient in meq of kcal = 400 × (60 / 1000)
= 4 × 6
= 24 meq of kcal
Hence, the patient receives 24meq of kcal amount of IV.
Learn more about amount here:
https://brainly.com/question/4567186
#SPJ1
Find the value of x.
Answer:
x = 52
Step-by-step explanation:
Since the inscribed angle measures 64 degrees, the minor arc is 64*2 = 128 degrees. Therefore the major arc is 180-128 = 232 degrees. Angle X is the difference of major and minor arc divided by 2, so X = (232-128)/2 = 52 degrees.
Which of the fallowing expressions represents the distance between -4 and 1
The answer is |-4 - 1|.
If you solve this absolute value, the answer would be 5 and if you look at the number line, the distance between the two dots is 5 units.
|-4 - 1| --> |-5| --> 5
in an absolute value, there are no negative numbers so the -5 becomes 5.
If Jamaal has 13 nickels and dimes in his pocket, and they have a combined value of 110 cents, how many
of each coin does he have?
dimes
nickels
0/4 pts 3 19 0
the equation of a circle given the center (–4, 4) and raduis r = 5.
Answer:
x² + y² + 8x - 8y + 7 = 0
Step-by-step explanation:
Formula: (x - a)² + (y - b)²= r²
where,
a = -4
b = 4
Substitute a and b
( x - (-4))² + (y - 4)² = 5²
(x + 4)² + (y - 4)² = 25
Open Bracket( )
(x + 4) (x + 4) = x² + 4x + 4x + 16
(y - 4) (y - 4) = y² - 4y - 4y + 16
x² + 4x + 4x + 16 + y² - 4y - 4y + 16= 25
Collect Like Terms
x² + y² + 8x - 8y + 16 + 16 - 25 = 0
x² + y² + 8x - 8y + 7 = 0
Therefore,
x² + y² + 8x - 8y + 7 = 0
Is The Equation Of The Given Circle.
Crane Manufacturing management is considering overhauling their existing line, which currently has both a book value and a salvage value of $0. It would cost $280,000 to overhaul the existing line, but this expenditure would extend its useful life to five years. The line would have a $0 salvage value at the end of five years. The overhaul outlay would be capitalized and depreciated using MACRS over three years. The tax rate is 35 percent, the opportunity cost of capital is 12 percent. The NPV of the new production line is $-360,000.
Since the cost of the renovation or overhauling of the existing line would be recovered in Year 4 and the NPV of the new production line is $-360,000, Crane Manufacturing should renovate.
What is the difference between renovation and replacement?Renovation restores an old asset to a better state. Replacement rids the old in preference for a new asset.
When the two investment options are weighed, a better choice can be arrived at.
Data and Calculations:MACRS - Three Years Depreciation:Year 1 = $93,324 ($280,000 x 33.33%)
Year 2 = $124,460 ($280,000 x 44.45%)
Year 3 = $41,468 ($280,000 x 14.81%)
Year 4 = $20,748 ($280,000 x 7.41%)
Total cost = $280,000
NPV of new production line = $-360,000
Thus, based on the cost recovery of the old production line and the negative NPV of the new production line, Crane Manufacturing should renovate.
Learn more about weighing investment decisions at https://brainly.com/question/12957049
#SPJ1
Question Completion:Should Crane replace or renovate the existing line?
BRIANLY FOR THE BEST EXPLANATION AND ANSWER!
Question: A circle has an area of 16mm². Find it's circumference.
Answer:
C ≈ 14.18
Step-by-step explanation:
Question Given:
A circle has an area of 16mm². Find it's circumference.
Formula:
C = 2√πA
Solve:
C = 2√πA
C = 2√(3.14 × 16)
C = 2√50.24
C = 14.1760361173
C ≈ 14.18
Hence, Circumference is approximately 14.18.
~Kavinsky
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Area of Circle :
[tex]\qquad \sf \dashrightarrow \: \pi {r}^{2} [/tex]
Now, it's given that area of circle is : 16 mm²
Let's calculate Radius ~
[tex]\qquad \sf \dashrightarrow \: \pi {r}^{2} = 16[/tex]
[tex] \qquad \sf \dashrightarrow \: {r}^{2} = \cfrac{16}{ \pi} [/tex]
[tex]\qquad \sf \dashrightarrow \: r = \sqrt{ \cfrac{16}{ \pi} } [/tex]
[tex]\qquad \sf \dashrightarrow \: r = { \cfrac{4}{ \sqrt{ \pi} } }[/tex]
Now,
[tex]\qquad \sf \dashrightarrow \: circumference = 2\pi r[/tex]
[tex]\qquad \sf \dashrightarrow \: c = 2 \pi \cfrac{4}{ \sqrt{ \pi} } [/tex]
[tex]\qquad \sf \dashrightarrow \: c = 8 \sqrt{ \pi} [/tex]
[ for approximate value take pi = 3.14 ]
[tex]\qquad \sf \dashrightarrow \: c = 8 \sqrt{3.14} [/tex]
[tex]\qquad \sf \dashrightarrow \: c \approx 8 \times 1.77[/tex]
[tex]\qquad \sf \dashrightarrow \: c \approx 14.18 \: \: mm[/tex]
What is the sum of 3x^3-2x+8,2x^2+5x,and x^3+2x^2-3x-3
Answer:
4x³ + 4x² + 5
Step-by-step explanation:
3x³ - 2x + 8 + 2x² + 5x + x³ + 2x² - 3x - 3.
4x³ - 2x + 8 + 2x² + 5x + 2x² - 3x - 3
4x³ + 4x² - 2x + 8 + 5x - 3x - 3
4x³ + 4x² + 8 - 3
4x³ + 4x² + 5
How many values are in the range?
0 to 50
find cube roots of -117 + 44i
By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.
How to find the cube root of a complex number
Herein we have a complex number in rectangular form, from which we need its magnitude (r) and direction (θ) and the De Moivre's formula as well. The root formula is introduced below:
[tex]z^{\frac{1}{n} } = r^{\frac{1}{n} }\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n}\right) +i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for k ∈ {0, 1, ..., n - 1} (1)
Where n is the grade of the complex root.
The magnitude and direction of the complex number are 125 and 0.886π radians, respectively. Thus, by the De Moivre's formula we obtain the following three solutions:
k = 0
z₁ = 2.997 + i 4.002
k = 1
z₂ = - 4.964 + i 0.595
k = 2
z₃ = 1.967 - i 4.597
By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.
To learn more on complex numbers: https://brainly.com/question/10251853
#SPJ1
add the two equations, 0.75x+1.5y=40 and −1.5x−1.5y=−60 , to find the value of x .
The value of x in the equation is 26.7
How to solve an equation?0.75x + 1.5y = 40
−1.5x − 1.5y = −60
add both equation to eliminate y .
Therefore,
−1.5x + 0.75x = -0.75x
1.5y + (- 1.5y) = 0
40 + (-60) = -20
Hence,
-0.75x = - 20
divide both sides by -0.75
-0.75x / -0/75 = - 20 / -0.75
x = - 20 / -0.75
x = 26.6666666667
x = 26.7
learn more on equation here: brainly.com/question/7234676
#SPJ1
Use a graphing tool to solve the equation for x. -4x − 1 = 5x + 4
Answer:
-5/9
Step-by-step explanation:
-4x - 1 = 5x +4 Add 4x to both sides
-1 = 9x + 4 Subtract 4 from both sides
-5 = 9x Divide both sides by 9
-5/9 = x
can someone give the exact answer for all the blanks
Considering the given function, we have that:
f(a) = 4 - 2a + 6a²f(a + h) = 6a² + 12ah + 6h² - 2a - 2h + 4.[f(a + h) - f(a)]/h = 12a + 6h - 2.What is the function for this problem?The function is:
f(x) = 4 - 2x + 6x².
When x = a, we have that:
f(a) = 4 - 2a + 6a².
When x = a + h, we have that:
f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.
For the fraction, we have that:
[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h
Hence:
[f(a + h) - f(a)]/h = 12a + 6h - 2.
More can be learned about functions at https://brainly.com/question/25537936
#SPJ1
Find the perimeter of the rectangle 2A+ 4
a
0
According to the Nielsen Media Research, of all the U.S. households that owned at least one television set, 83% had two or more sets, A local cable
company canvassing the town to promote a new cable service found that the 300 randomly selected households visited, 240 had two or more
television sets. At 0.05 level of significance, is there sufficient evidence to conclude that the proportion is less than the one in the report?
Answer Questions 12-23.
The level of significance on 0.05 exists at 83%.
How to find the level of significance?The sample size (n) specified by the local cable company exists 300 which exists quite large.
According to the Central limit theorem, the sampling distribution of sample proportion observes a normal distribution with mean p and standard deviation
[tex]$\sqrt{\frac{p(1-p)}{n}}$[/tex]
Since the sampling distribution of sample proportions observes a normal distribution utilize the z-test for one proportion to execute the test.
The hypothesis is:
[tex]$H_{0}$[/tex]: The proportion of U.S. households that owned two or more televisions exists at 83 %, i.e. p = 0.83
[tex]$H_{1}$[/tex]: The proportion of U.S. households that owned two or more televisions exists less than 83 %, i.e. p < 0.83
Decision Rule:
At the level of significance [tex]$\alpha=0.05$[/tex] the critical region for a one-tailed z-test is:
[tex]$Z \leq-1.645[/tex]
By using the z table for the critical values.
So, if [tex]$Z \leq-1.645$[/tex] the null hypothesis will be rejected.
Test statistic value:
[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
Here [tex]$\hat{p}$[/tex] exists the sample proportion.
Compute the value of [tex]$\hat{p}$[/tex] as follows:
[tex]$&\hat{p}=\frac{X}{n} \\[/tex] [tex]$&=\frac{240}{300} \\[/tex]
= 0.80
To compute the value of the test statistic as follows:
[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]
[tex]$=\frac{0.80-0.83}{\sqrt{\frac{0.83 \cdot(1-0.83)}{3000}}}$[/tex]
The test statistic exists at -1.383 which exists more than -1.645.
Therefore, the test statistic lies in the acceptance region.
Thus we fail to reject the null hypothesis.
At a 0.05 level of significance, we fail to reject the null hypothesis noting that the proportion of U.S. households that owned two or more televisions exists at 83%.
To learn more about the level of significance refer to:
https://brainly.com/question/9163177
#SPJ9
The difference of the square of a number and 36 is equal to 5 times that number. Find the positive solution.
Answer:
x=-4, x=9
Step-by-step explanation:
We write this into words:
difference = subtraction
square = ^2
a number = x
is equal to = =
5 times that number = 5x
x^2-36 = 5x
write in standard form
x^2-5x-36
what adds to -5 and multiplies to -36?
-9 and 4!
(x-9)(x+4)
x-9 = 0
x= 9
x+4 = 0
x=-4
Answer:
9
Step-by-step explanation:
Let the number = x.
x² - 36 = 5x
x² - 5x - 36 = 0
(x - 9)(x + 4) =0
x = 9 or x = -4
Answer: 9
Two companies working together can clear a parcel of land in 8 hours. Working alone, it would take Company A 4 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone?
The time taken for Company B to clear the parcel of land alone is 14.25 hours
Rate of workTime for Company B to clear the parcel of land alone = xCompany B work rate = 1/xTime for Company A to clear the parcel of land alone = x + 4Company A work rate = 1/x+4Time for both Company to clear the parcel of land alone = 8 hoursBoth Company work rate = 1/81/8 = 1/x + 1/(x + 4)
1/8 = (x+4)+ (x) / (x)(x+4)
1/8 = (x+4+x) / (x² + 4x)
1/8 = 2x+4 / (x² + 4x)
cross product
1(x² + 4x) = 8(2x + 4)
x² + 4x = 16x + 32
x² + 4x - 16x - 32 = 0
x² - 12x - 32 = 0
Using quadratic formula
x = 14.25 or -2.25
The time taken for Company B to clear the parcel of land alone can only be positive,
Therefore, it is 14.25 hours
Learn more about rate of work:
https://brainly.com/question/169382
#SPJ1
Bags of chips cost $4 each. Write a direct
proportion equation using (b) for bags of
chips and (t) for total cost.
Answer:
t = 4b
Step-by-step explanation:
Each bag costs 4 dollars.
hope this helps! <3