Using algebraic expressions, we figured out that Thomas has 74 quarters and 82 dimes in his change jar, based on the total value of $26.70 and the fact that he has 8 more dimes than quarters.
Explanation:To solve the problem involving the collection of dimes and quarters in Thomas's change jar, we need to use algebra. Let's define the variables first: let q be the number of quarters and q + 8 be the number of dimes since Thomas has 8 more dimes than quarters.
Since each quarter is worth $0.25 and each dime is worth $0.10, we can set up the following equation to represent the total amount of money ($26.70):
0.25q + 0.10(q + 8) = 26.70
Now, we simply solve for q:
Multiply each term within the parenthesis by 0.10:0.25q + 0.10q + 0.80 = 26.70Combine like terms:0.35q + 0.80 = 26.70Subtract 0.80 from both sides to isolate the variable term:0.35q = 25.90Divide both sides by 0.35 to find q:q = 25.90 / 0.35q = 74Therefore, Thomas has 74 quarters. To find the number of dimes:
q + 8 = 74 + 8 = 82
Thus, Thomas has 82 dimes.
Thomas's change jar has a total of 74 quarters and 82 dimes.
What type of angles are 6 and 8?
Y -2 > -11 what is the answer to this
Factor this expression: ab + 4 + a + 4b
Grouping method works best on this one:
ab+a+4+4b=a(b+1)+4(b+1)
=(a+4)(b+1)
Answer:
Grouping method works best on this one:
ab+a+4+4b=a(b+1)+4(b+1)
=(a+4)(b+1)
Step-by-step explanation:
How to tell if an equation has no solution without solving?
In a study of a weight loss program, 40 subjects lost a mean of 3.0 lb after 12 months. Does the weight loss program have statistical significance? In a study of a weight loss program, 40 subjects lost a mean of 3.0 lb after 12 months. Does the weight loss program have statistical significance?
Answer:
The weight loss program is statistically significant.
Step-by-step explanation:
We can define a statistically significant difference or result as a result which is not attributed to chance. In other words we can say that a statistical significance shows if the difference observed between groups is real or if it has occurred simply due to chance.
Here, given is that 40 subjects lost a mean of 3.0 lb after 12 months.
So, here the weight loss program is statistically significant as the results are unlikely to occur by chance.
The blade of a circular saw rotates at a rate of \2500 revolutions per minute. what is the linear velocity in miles per hour of a point on the tip of the outer edge of a 7 and one fourth7 1 4 inch diameter blade?
The linear velocity of a point on the tip of the outer edge of the circular saw blade is 0.429 miles per hour.
Explanation:To find the linear velocity of a point on the tip of the outer edge of the circular saw blade, we can use the formula:
Linear velocity = 2 * π * radius * angular velocity
Where the radius is half of the diameter. Given that the diameter is 7 1/4 inches, the radius is 7 1/4 / 2 = 3 5/8 inches or 3.625 inches. Converting this to feet, we get 3.625 / 12 = 0.302 feet. To convert the angular velocity from revolutions per minute to radians per second, we multiply by 2 * π / 60. Substituting these values into the formula, we get:
Linear velocity = 2 * π * 0.302 * (2500 * 2 * π / 60) = 37.699 feet per minute.
To convert this to miles per hour, we divide by 5280 (since there are 5280 feet in a mile) and multiply by 60 (since there are 60 minutes in an hour):
Linear velocity = (37.699 / 5280) * 60 = 0.429 miles per hour.
What is the value of x
for the function:
f(x) = -3x^4
complete the table of values using at least 5 points.
x -2 -1 0 1 2
f(x)
How to solve it using the system of substitution
find an angle measure that is supplementary to this angle 126 degrees
Answer:
Step-by-step explanation:
Answer:
54°
Step-by-step explanation:
The sum of the measures of two supplementary angles is 180°.
180° - 126° = 54°
Answer: 54°
150 adults complete a survey. 80 are women. Write the ratio men:women in its simplest form?
Total number of adults are 150 that complete the survey in which 80 are women and 70 are men and the ratio of men:women in its simplest form is 7:8 which can be determine by using simple arithmetic operations.
Given :
Total number of adults = 150.
Total number of Women = 80.
Arithmetic operations can be use to determine the total number of Men. To evaluate the total number of men following steps can be use:
Step 1 - Let the total number of men be x.Step 2 - Now, the total number of adults is 150 that is:150 = x + 80 ---- (1)
Step 3 - Subtract 80 from both the sides of the equation (1).150 - 80 = x + 80 - 80
70 = x
Therefore, the total number of men present in 150 adults are 70. Now, the ratio of men:women is given by:
[tex]\rm \dfrac{men}{women} = \dfrac{70}{80}[/tex]
[tex]\rm \dfrac{men}{women } = \dfrac{7}{8}[/tex]
So, the ratio men:women in its simplest form is 7:8.
For more information, refer the link given below
https://brainly.com/question/22687297
What is the slope of a line that is perpendicular to a line whose equation is 3y=−4x+2 ?
Enter your answer in the box.
Answer:
the slope is 3/4
Step-by-step explanation:
the slope is 3/4 because 3 is the y line and 4 is the x line giving you 3/4 as your slope.
The slope of the line that is perpendicular to a line whose equation is 3y=−4x+2 is 3/4
The given line equation is:
3y = -4x + 2
Express the equation in the point-slope form of a line equation
The point-slope form of the equation of a line is y = mx + c
where m represents the slope
and c represents the y-intercept
3y = -4x + 2
[tex]y = \frac{-4}{3}x +\frac{2}{3}[/tex]
Comparing the equation [tex]y = \frac{-4}{3}x +\frac{2}{3}[/tex] with y = mx + c:
The slope, m = -4/3
The slope of the line perpendicular to [tex]y = \frac{-4}{3}x +\frac{2}{3}[/tex] will be:
[tex]m_2= \frac{-1}{m} \\\\m_2= \frac{-1}{\frac{-4}{3} }\\\\m_2 = \frac{3}{4}[/tex]
The slope of the line that is perpendicular to a line whose equation is 3y=−4x+2 is 3/4
Learn more here: https://brainly.com/question/1417258
Which is the quadratic variation equation for the relationship y varies directly with x^2 and y=72 when x=3
y =72
x = 3
X^2 = 3^2 = 9
k = y/x = 72/9 =8
so you should have an option of:
y =8x^2
(y3 - 4y2 + 7y - 6) ÷ (y - 2)
What is 2(6+5•2)=5(4-2•5)
Answer: Not true
Step-by-step explanation: 2(16)=5(-6)
32=-30
This is not true
Lets find F^(-1) if
y=-2x+1
I’m not sure if the F^(-1)=1+x/2
A set of positive and negative rational numbers are shown. 715 , –215 , 1115 , 415 , –815 What is the difference between the largest and the smallest numbers in the list?
5. A piece of plywood has a length that is 5 more than twice its width. Write the expression that represents the area of the plywood.
Else's math class has 11 female students and 10 male students.Write the ratio of female students to the total number of students in two different ways.
The detailed answer explains how to write the ratio of female students to the total number of students in two different ways.
The ratio of female students to the total number of students:
11 female students to 21 total students: 11/21
Alternatively, you can simplify the ratio to 1 female student to 2 total students: 1/2
Please help me with this!!
The coefficients of the expression 5x^4-4x^2+3 are??
Write 3 ½% as a fraction
Answer:
7/200
Step-by-step explanation:
3.5% = 3.5/100 = (3.5/100)×(2/2) = 7/200
_____
The % symbol is a shorthand way to write "/100", so 3.5% = 3.5/100.
Dani is working a sample booth at the national soda and beverage convention. She is paid $1.50 for each of the first ten tastings $2.50 for each of the next twenty tastings and $4.00 for each tasting beyond thirty she conducts each day. Today Dani conducted 36 tastings. How much total pay did Dani earn today?
What is an equation of the line in slope-intercept form? m = 2 and the y-intercept is (0, 3)
The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers?
Which three expressions could be used to represent the numbers?
n; n - 4; 4n
n; 4 - n; n + 4
n; n/4; n + 4
An ion has a charge of +7. How far is it from being neutral?
A. -0.07
B. -7
C. 7
D. 70
E. 0.7
Answer:
B. -7
Step-by-step explanation:
An atom has a neutral charge with equal numbers of positive and negative particles,
That is, an atom with no chargen or 0 charge is called neutral.
Given,
The ion has a charge of +7,
Also, + 7 - 7 = 0,
Thus, for being neutral the ion needs -7 charge,
Hence, option 'B' is correct.
How many solutions are there?
A card is drawn from a standard deck of 52 playing cards. find the probability that the card is an ace or a black card.
The probability that the card is an ace or a black card is 7/13
Probability is the likelihood or chance that an event will occur.
A standard card contains 52 cards. Hence the total outcome is 52.
Since there are 4 aces, the expected outcome is 4The total number of black cards is 26The total card that is ace and black is 2Get the required probability;
Prob(ace or black card) = Prob(ace) + Prob(black card) - P(ace and black card)
Prob(ace or black card) = 4/52 + 26/52 -2/52
Prob(ace or black card) = 28/52
Hence the probability that the card is an ace or a black card is 7/13
Learn more on probability here: https://brainly.com/question/14192140
Please do not make into a fraction because I can’t use a fraction as an answer. Rewrite using a negative exponent.
1/(xy)^1
The graph of a line goes up and to the right when
Answer: When the coefficient of X is positive!