The algebraic expression for the word phrase '8.46 less than the product of 42 and x' is '42x - 8.46'. The phrase 'less than' means to subtract the number from the result of the multiplication.
Explanation:The process of writing an algebraic expression involves converting the given word phrase into mathematical symbols and operations. In this case, the word phrase is '8.46 less than the product of 42 and x'. 'Product' in mathematics means multiplication so 'the product of 42 and x' could be written as '42x'. 'Less than' means to subtract, but the order matters. '8.46 less than' means we subtract 8.46 from our product, not the other way around. Therefore, the algebraic expression for this word phrase is '42x - 8.46'.
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A washer and a dryer cost $917 combined. The washer costs $67 more than the dryer. What is the cost of the dryer?
To find the cost of the dryer, set up equations based on the given information and solve for the dryer's cost, which results in the dryer being priced at $425.
Explanation:To solve for the cost of the dryer in the given problem, we can create two equations based on the information provided. Let's denote the cost of the dryer as D and the cost of the washer as W. According to the problem, W = D + $67, and the combined cost of the washer and dryer is $917, so W + D = $917.
Substituting the first equation into the second, we have (D + $67) + D = $917. Simplifying this, we get 2D + $67 = $917. Subtracting $67 from both sides of the equation gives us 2D = $850. Finally, dividing both sides by 2, we find that D = $425.
Therefore, the cost of the dryer is $425.
The distance from NYC to Margate, New jersey on our route is 130 miles. Use the equation (d = 60t) to find t, the time needed to drive the distance.
What number has the same value as 32 tens
What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept? The slope is and contains the point (0, 2). The slope is and contains the point (0, −2). The slope is and contains the point (0, 2). The slope is and contains the point (0, −2).
Answer: D.)The slope is Negative three-halves and contains the point (0, −2).
Step-by-step explanation:
i got it correct obviously oncrip
Emelina wrote the equation of a line in point-slope form as shown below. (y+4)=3(x+2) What is Emelina’s equation in slope-intercept form?
Answer:
[tex]y=3x+2[/tex]
Step-by-step explanation:
We are given equation as
[tex](y+4)=3(x+2)[/tex]
Since, we have to write equation in slope-intercept form
so, we can use slope-intercept formula
[tex]y=mx+b[/tex]
where m is a slope
b is y-intercept
so, we can write our equation in this form
[tex](y+4)=3(x+2)[/tex]
Distribute 3
[tex]y+4=3\times x+3\times 2[/tex]
[tex]y+4=3x+6[/tex]
Subtract both sides by 4
[tex]y+4-4=3x+6-4[/tex]
[tex]y+4-4=3x+6-4[/tex]
[tex]y=3x+2[/tex]
So, slope-intercept form of equation is
[tex]y=3x+2[/tex]
A brownie recipe asks for one and one quarter times as much sugar as chocolate chips. If one and two thirds cups of sugar is used, what quantity of chocolate chips would then be needed, according to the recipe?
Final answer:
To determine the quantity of chocolate chips needed for a recipe that calls for one and one quarter times as much sugar as chocolate chips, set up a proportion using the given sugar amount. Multiply the sugar quantity (1⅓ cups) by the reciprocal of the ratio (4/5), which results in 1⅓ cups of chocolate chips needed.
Explanation:
To determine the quantity of chocolate chips needed when the recipe asks for one and one quarter times as much sugar as chocolate chips, we can use a simple proportion based on the quantity of sugar used. The recipe specifies that 1⅔ cups of sugar are used, which is equivalent to ⅓ cups of sugar when converted to an improper fraction.
The proportion would look like this: Chocolate Chips (C) is to 1 as 1⅓ cups of sugar is to 1⅔, which can be set up as a ratio: C/1 = (1⅓)/(1⅔). To solve for C, we multiply both sides by 1 to get rid of the denominator for C, giving us:
C = (1⅓)/(1⅔)
Now, let's solve the equation:
Convert 1⅓ to an improper fraction: 5/3.
Convert 1⅔ to an improper fraction: 5/4.
Divide 5/3 by 5/4 to find the quantity of chocolate chips: (5/3) × (4/5) = 20/15 = 4/3, which simplifies to 1⅓ cups.
Therefore, you would need 1⅓ cups of chocolate chips for the recipe.
For a population, the mean is 19.4 and the standard deviation is 5.8. Compare the mean and standard deviation of the following random samples to the population parameters.
25, 32, 16, 12, 11, 38, 22, 21, 19, 20
Answer:
The mean of sample (21.6) is greater than population mean and the standard deviation of sample (8.4) is also greater than population standard deviation.
Both values, mean and std are greater than corresponding population values. This means, that our sample overestimates or is skewed to the right in the values of population. Also each specific value is farther apart from the mean so variation is much bigger in our sample than in our population.
Step-by-step explanation:
To calculate the mean, we estimate the avergage of the data as
Mean = Sum(data)/n
Where n is the number of observations of sample. We have;
(25 + 32 + 16 + 12 + 11 + 38 + 22 + 21 + 19 + 20)/10 = 21.6
The standard deviation is the square root of variance. Variance is sum of the deviation of each data point to the sample mean.
Variance = sum i= 1 to n (Xi-xmean)/(n-1)
Where n = 10 the # of observations and xi is each specific data point.
If you calculate it in Excel or or by hand you obtain:
Variance = sum i= 1 to n (Xi-21.6)/(10-1) = 8.4
Both values, mean and std are greater than corresponding population values. This means, that our sample overestimates or is skewed to the right in the values of population. Also each specific value is farther apart from the mean so variation is much bigger in our sample than in our population.
Answer:
The mean of the random samples (21.6) is greater than population´s mean (19.4) and the STD of the random samples (7.96) is greater than population´s STD (5.8)
Step-by-step explanation:
To calculate the mean of the random samples, we find the average value of the data set
[tex]Mean=\frac{(\sum_{i=0}^{n}{a_i})}{n}\\[/tex]
Where a is an element of the random example and n is the number of elements in the sample, as follows
Mean = (25+32+16+12+11+38+22+21+19+20)*(1/10) = 21.6
To calculate the STD (Standard Deviation) we need to know the variance, because
[tex]STD=\sqrt{var}[/tex]
The variance is determined as the sum of the deviation from one element of the data to the mean squared, all divided by n as below.
[tex]Var=(\sum_{i=1}^{n}{(a_{i}-Mean)^{2})/n[/tex]
If you calculate this by calculator or with a computer, you should get Var=63.44
And with that value, STD=7.96≈8
Therefore, by comparison, both Mean and STD of the random sample are greater than the population´s parameter
what is 11x-(6x-5)=40
Need answer to number six in this photo
Sergio's internet provider charges its customers $9 per month plus 4¢ per minute of on-line usage. Sergio received a bill from the provider covering a period and was charged a total of $81.40. How many minutes did he spend on-line during that period? (Round to the nearest whole minute, if necessary.)
A restaurant advertises 256 types of nachos. how many topping ingredients must be available
In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order de y'' − y = 0. find a solution of the second-order ivp consisting of this differential equation and the given initial conditions. y(0) = 1, y'(0)= 8
Find n(A) for A={0,1,2,3,...,2000}
Final answer:
To find n(A), we count the elements in the set A={0,1,2,3,...,2000} which form an arithmetic sequence. By applying the formula for the number of terms in an arithmetic sequence, we find that n(A) = 2001.
Explanation:
To find n(A), which represents the number of elements in set A, we simply count the elements listed in the given set A={0,1,2,3,...,2000}. These elements form an arithmetic sequence starting from 0 and ending at 2000 with a common difference of 1 between each consecutive number.
The formula for the number of terms n in an arithmetic sequence is given by:
n = (last term - first term) / (common difference) + 1
Applying the formula to our set A:
n = (2000 - 0) / 1 + 1 = 2000 + 1 = 2001
Therefore, n(A) = 2001.
use rounding or compatible numbers to estimate the sum 171+ 727
Is 9760-5,220 more or less then 4,000
Answer:
9760-5220 is more than 4000.
Step-by-step explanation:
Consider the provided numbers.
We need to find 9760-5220 is more or less than 4000.
Subtract the numbers as shown.
9760
-5220
4540
Now compare the number 4540 and 4000
By comparing it can be concluded that the number 4540 is greater than 4000.
Hence, 9760-5220 is more than 4000.
After working for 25 hours lammer made $375 after working 40 hours lammer made $600 predict how much will he make after 10 hours of work
Lammer will make $150 after working for 10 hours .
Calculating Earnings Based on Hours Worked
To predict how much Lammer will make after working 10 hours, we first need to determine his hourly wage. From the information given, we know:
After working 25 hours, Lammer made $375.After working 40 hours, Lammer made $600.We can calculate his hourly wage as follows:
Hourly Wage = Total Earnings / Total Hours Worked
For both inputs, we observe:
$375 / 25 hours = $15 per hour$600 / 40 hours = $15 per hourThis indicates that Lammer's hourly wage is consistent at $15 per hour.
Now, to predict how much he will make after working 10 hours:
Earnings for 10 Hours of Work = Hourly Wage x Number of Hours
Earnings for 10 Hours = $15 x 10 = $150
Therefore, Lammer will make $150 after working 10 hours.
You want to get out of the sun and look for some shade. There are some trees by the side of the lake. You know you are just below 2 metres in height.
Estimate the height of the tree in metres.
Algebra 2 Slope questions
A projectile is shot from a cannon. The fixed parameters are the acceleration of gravity, g=9.8 m/sec2, and the muzzle velocity, v0=500 m/sec, at which the projectile leaves the cannon. The angle θ, in degrees, between the muzzle of the cannon and the ground can vary. The range of the projectile is
f(θ)=vo^2/g sin πθ/90=25510 sin πθ/90 meters.
The range at θ = 10⁰ is 155.4 meters.
What is a projectile?
A projectile is an object thrown or projected into the air, subject to gravity, following a curved trajectory.
Given that
v₀ = 500m/s
g = 9.8 m/s²
θ = 10⁰
Substitute into the function
f(θ)=v₀²/g sin πθ/90=25510 sin πθ/90 meters.
f(θ)= 25510sin πθ/90
= 25510sin10π/90
= 25510sinπ/9
= 25510sin(3.142/9)
= 25510sin(0.349)
= 25510 * 0.00609
= 155.4 m
The range at θ = 10⁰ is 155.4 meters.
Complete question
The greater the initial velocity of a projectile, the greater the range, with the maximum range achieved at a 45° angle in the absence of air resistance.
Explanation:The initial velocity of a projectile has a significant impact on its range. Specifically, the greater the initial speed, ℓ0, the greater the range. The formula for range R on level ground, neglecting air resistance, is given by R = (v0²/g) sin(2θ), where θ is the launch angle, v0 is the initial velocity, and g is the acceleration due to gravity. The maximum range is reached when the launch angle is 45°. With air resistance, the optimal angle decreases to roughly 38°. Additionally, for every angle other than the optimal, there are two different angles that yield the same range, and their sum totals 90°.
27x to second power-42x+12 if x=2
an insurance company sells a policy that pays $50,000.00 in case of accidental death. According to company figures, the rate of accidental death is 47 per 100,000 each year. What annual premium should the company charge for this coverage?
What is the range of the function y=4e^x
the answer (B) thank me later ;)
Find the linear function such that f(1)=8 and f(5)=-4
What is the value of m?
1/3m+3−5/6m=−15
The value of m is 36
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation.
Given:
1/3m+3−5/6m=−15
Subtract 3 from both sides
1/3m +3 -5m/6 -3= -15-3
Simplify
1/3 m -5m /6 = -18
Now, multiply the LCM
-3m = -108
Divide both side by (-3)
-3m/(-3)= -108/ (-3)
m= 36.
Hence, the value of m is 36.
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Evaluate the numerical expression 36÷14-5-10-7
What pair of fractions is 0.8 between on a number line
What is 3a squared add 7 a
Need help finding the limit as x approaches 0 of (x^2-3sin(x)/x)
will give BRAINEST
A function has a constant halving time. What type of function does this represent?
Answer:
Exponential decay
Step-by-step explanation:
The function which has a constant halving time represents the exponential decay or negative growth curve type of function.
What is exponential decay?When the value of one variable of the function is decreased with increase in the number of other variable, then it is called the exponential decay function with constant exponential coefficient.'
It can be given as,
[tex]f(x)=ab^x[/tex]
Here, a is the exponential coefficient.
A function which has a constant halving time is,
[tex]A(t)=A_o\left(\dfrac{1}{2}\right)^{t/h}[/tex]
Here, Ao is the initial time, t is time and h is halving time. This is an exponential decay function.
The function which has a constant halving time represents the exponential decay or negative growth curve type of function.
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greatest common factor for 8x and 40