Each measure in a 4/4 time signature has four quarter note beats; each measure in a ¾ time signature has three quarter note beats; and each measure in a 2/4 time signature has two quarter note beats.
How many beats are in each of these measures?A 4/4 time signature does not imply that each measure contains simply four quarter notes. It signifies that each measure only contains four beats. These beats may comprise half notes, quarter notes, eighth notes, pauses, or whatever the composer desires, but all note and rest values must add up to no more or less than the time signature’s top number (or numerator).
The most popular musical meter is 4/4. Because it is so widespread, it is also known as common time, and the two numerals in the time signature are sometimes substituted with the letter C. The stacking digits in 4/4 indicate that each measure comprises four quarter note beats. To count 4/4 meter, tap the beat every time you tap the beat.
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3xsquared minus 5 equals negative 5x minus 3
Answer:
see below
Step-by-step explanation:
3²-5 = -5x-3
9-5 =- 5x-3
-5x = 7
so x= -7/5
Jennifer opened a savings account and deposited $300.00. The account earns 13% interest, compounded monthly. If she wants to use the money to buy a new bicycle in 2 years, how much will she be able to spend on the bike?
If Jennifer wants to use the money to buy a new bicycle in 2 years, she can spend (future value) $388.54 on the bike as the account earns 13% interest, compounded monthly.
What is compounded interest?Compound interest is a system of interest computation where interest accumulates on the principal and previously accumulated interests.
Compounding the present value means adding interest to the principal amount when calculating subsequent interests.
N (# of periods) = 24 months (2 years x 12)
I/Y (Interest per year) = 13%
PV (Present Value) = $300
PMT (Periodic Payment) = $0
Results:
Future Value (F) = $388.54
Total Interest = $88.54
Thus, with a deposit of $300, Jennifer can spend $388.54 after earning 13% monthly compounded interest.
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An investigator has a computer file showing family incomes for 1,000 sub- jects in a certain study. These range from $5,800 a year to $98,600 a year. By accident, the highest income in the file gets changed to $986,000. (a) Does this affect the average? If so, by how much? (b) Does this affect the median? If so, by how much?
Jessica invests $3,065 in a savings account with an annual interest rate of 5% compounded continuously. What will the account balance be after 5 years? Round to the nearest dollar
The account balance after 5 years will be $3935.53.
What is compound interest?Compound interest is interest that is paid on both principal and interest at regular intervals. The first year of compound interest is similar to the first year of simple interest, but the difference begins in the second year.
Continuously compounded interest means that an account balance is constantly earning interest and reinvesting that interest so that it, too, earns interest.
Given that Jessica invests $3,065 in a savings account with an annual interest rate of 5% compounded continuously.
The account balance after 5 years will be calculated as:-
[tex]P(t) = P_oe^{rt}\\P(t) = 3065\times e^{0.05\times 5}\\P(t) = \$3935.53[/tex]
Therefore, the balance in the account after 5 years will be $3935.53.
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HELP ASAP! FIND LINEAR EQUATION PARALLEL TO Y = -3/4X + 1 THROUGH POINTS (8,-6)
Answer:
y = [tex]-\frac{3}{4}[/tex] x
Step-by-step explanation:
y = mx + b , where "m" is a slope and "b" is an y-intercept.
If a║b ⇒ [tex]m_{a}[/tex] = [tex]m_{b}[/tex] and [tex]b_{a}[/tex] ≠ [tex]b_{b}[/tex]
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~
y = [tex]-\frac{3}{4}[/tex] x + 1
( 8 , - 6 )
y - ( - 6 ) = [tex]-\frac{3}{4}[/tex] ( x - 8 )
y + 6 = [tex]-\frac{3}{4}[/tex] x + 6
y = [tex]-\frac{3}{4}[/tex] x
you have found the following ages( in years)of 5 porcupines?
what is the standard deviation? round your answers to the nearest tenth
The standard deviation is 4.0, while mean is 10.2.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Mean = 10.2
The standard deviation is 4.0.
Age in the mean is the average age.
Mean = (16 + 10 + 5 + 7 + 13)/5
Mean = 51/5 = 10.2
The variance's square root will reveal the standard deviation.
(16 - 10.2) + (10 -10.2) + (5-10.2) + (7-10.2)+( 13-10.2) ( 13-10.2)
5.8 + 0.2 -5.2 - 3.2 + 2.8
each number into squares
33.64 + 0.04 + 27.04 + 10.24 + 7.84
Variation: 78.8/5 = 15.76
Standard deviation = 3.969 = 4.0.
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The complete question is,
16, 10, 5, 7, 13
What is the porcupines' typical age based on your sample? Where can I find the standard deviation? in a circle tenths of a percent, closest.
Use a graphing utility to graph the function to approximate (to two decimal places) any relative minima or maxima of the function. (If an answer does not exist, enter DNE.)
h(x) = x3 − 6x2 + 16
Answer:Use a graphing utility to graph the function and approximate (to two decimal places) any relative minima or maxima. (If an answer does not exist, enter DNE.)
f
(
x
)
=
x
3
−
3
x
2
−
x
+
3
relative minimum
(
x
,
y
)
=
c
Step-by-step explanation:
there is a right triangle abc, where
If the sum of the squares on its other two sides equals the square of its greatest side.
Given:
AB = 9 cm CB = 40 cm AC = 41 cm
The Pythagorean Theorem states that
If the largest side's square is equal to the sum of the squares on the other two sides, the triangle will have a right angle.
AB = 9 cm CB = 40 cm AC = 41 cm
The Pythagorean Theorem states that
AC 2 =BC² +AB ²
41²=40²+9²
41 ²=40 ² +9 ²
1681 = 1600 + 81
1681 = 1681
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The question is incomplete
Show that the triangle ABC is a right-angled triangle; if:
AB = 9 cm, BC = 40 cm, and AC = 41 cm.
In 2007, there were 120 houses in a subdivision. The number of houses in the subdivision increased by approximately 8% per year from 2007-2017. Enter the BEST estimate of the number of houses in the subdivision in 2017.
Answer:
216
Step-by-step explanation:
2017-2007=10
8*10=80
80% of 120= 96
120+96=216
help please she didn’t teach us thistle
Answer:
12x^4y^7
Step-by-step explanation:
base(b)=8x^3y^5
height(h) =3xy^2
Area= (b x h)/2 =12x^4y^7
Answer:
[tex]A = 12x^4y^7[/tex]
Step-by-step explanation:
The formula for the area of a triangle is:
[tex]A = \dfrac{1}{2}bh[/tex]
where [tex]b[/tex] is the length of the triangle's base and [tex]h[/tex] is the length of the triangle's height.
In this problem, we are given the length of the base of the triangle as [tex]8x^3y^5[/tex] and the length of the height of the triangle as [tex]3xy^2[/tex].
Thus, the area of the given triangle is:
[tex]A = \dfrac{1}{2} \cdot 8x^3y^5 \cdot 3xy^2[/tex]
We can simplify this by combining like terms and using the exponent addition rule ([tex]x^a \cdot x^b = x^{a+b}[/tex]).
[tex]A =\left(\dfrac{1}{2} \cdot 8 \cdot 3 \right)(x^3 \cdot x)(y^5 \cdot y^2)[/tex]
[tex]A = (4 \cdot 3)(x^{3 + 1})(y^{5+2})[/tex]
[tex]A = 12x^4y^7[/tex]
When a test is ________
If the value of interest falls outside a 95% confidence interval, we will reject the null hypothesis at the a =______ significance level If the value of interest falls outside a 99% confidence interval, we will reject the null hypothesis at the =_____< significance level
When a test is two-sided and one-sided: We will reject the null hypothesis at the = X 0.01 0.050. 10 significance level if the value of interest falls outside a 95% confidence interval. If the value of interest falls outside a 99% confidence interval, the null hypothesis will be rejected at the = 0.010.
What is confidence interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used. The confidence interval is the range of values within which you expect your estimate to fall a certain percentage of the time if you repeat your experiment or re-sample the population in the same manner.
Here,
When a test is two-sided and one-sided: If the value of interest falls outside a 95% confidence interval, we will reject the null hypothesis at the = X 0.01 0.050. 10 significance level. The null hypothesis will be rejected at = 0.010 if the value of interest falls outside a 99% confidence interval.
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Answer:
two sided.
.05
.01
Step-by-step explanation:
Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors.
if b is the span of the given vectors, so we can express b as the linear combination of the other given two vector.
given that,
[tex]a_{1} =\left[\begin{array}{ccc}-1&\\3&\\-1\end{array}\right] , a_{2} =\left[\begin{array}{ccc}-2\\-3\\6\end{array}\right] , b=\left[\begin{array}{ccc}-6\\9\\2\end{array}\right] \\\\\\\\\\\\\\\\\\\\\\\\[/tex]
We have determined that b is span of given vector a1 and a2.
we can write. [tex]a_{1} =(-1,-3,-1) ,a_{2}=(-2,-3,6) , b=(-6,9,2)[/tex] .
A vector is a quantity that has magnitude and direction.
if x,y,z...., v are vectors and a,b,c....k are scalars then the linear combination is ax+by+cz+......+kv
The set of linear combinations is called span for set of vectors.
So, b is span of given vector.
[tex]b=(c)a_{1} +(d)a_{2}[/tex] ...... equation (A)
where c and d are scalars.
Now,
[tex](-6,9,2)=c(-1,3,-1)+d(-2,-3,6)\\(-6,9,2)=(-c,3c,-c)+(-2d,-3d,6d)\\(-6,9,2)=(-c-2d,3c-3d,-c+6d)\\[/tex]
equating the equations,
[tex]-c-2d=-6\\3c-3d=9\\-c+6d=2\\[/tex]
now we shall solve the above linear equations.[tex]subtract \\-c-2d-(-c+6d) = -6-2\\-8d=-8\\d=1\\now, \-c=-6+2d\\c=6-2=4\\c=4[/tex]
So, value of scalars c, d satisfied equation A,
thus, b is span of given vector a1 and a2.
The complete question is.
Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors. a1=[-1 3 -1], a2=[-2 -3 6]= [-6 9 2]
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answer now for brainliest its my last one
The missing length is given as follows:
LN = 44.
How to obtain the missing length?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
The parallel lines for this triangle are given as follows:
VU and LM.
Hence the proportional relationship regarding the remaining side lengths is given as follows:
x/24 = 11/8
Applying cross multiplication, we have that:
8x = 24 x 11
x = 3 x 11
x = 33.
Hence the missing length is given as follows:
LN = 33 + 11
LN = 44.
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In a population of bats living in a certain region, 30 percent have a wingspan greater than 10 inches. In a random sample of 80 bats living outside of the region, 20 had a wingspan greater than 10 inches. Consider a one-sample z-test to investigate whether there is evidence that the proportion of bats with a wingspan greater than 10 inches living outside the region is different from that of the bats living in the region. Which of the following is the correct test statistic?
answer choices
z=\frac{0.30-0.25}{\sqrt{\frac{\left(0.25\right)\left(0.75\right)}{80}}}
z= 80
(0.25)(0.75)
0.30−0.25
z=\frac{0.30-0.25}{\sqrt{\frac{\left(0.30\right)\left(0.70\right)}{80}}}
z= 80
(0.30)(0.70)
0.30−0.25
z=\frac{0.25-0.30}{\sqrt{\frac{\left(0.25\right)\left(0.75\right)}{80}}}
z= 80
(0.25)(0.75)
0.25−0.30
z=\frac{0.25-0.30}{\sqrt{\frac{\left(0.25\right)\left(0.75\right)}{80}}}
z= 80
(0.25)(0.75)
0.25−0.30
z=\frac{0.25-0.30}{\sqrt{\frac{\left(0.30\right)\left(0.70\right)}{80}}}
z= 80
(0.30)(0.70)
0.25−0.30
The correct static test is [tex]$z=\frac{0.30-0.25}{\sqrt{\frac{0.30(0.70)}{80}}}$[/tex]
What is static test?Without actually running the software application's code, static testing is a type of software testing technique used to check for errors in software. The code is run to find the flaws in Dynamic Testing tests, though. To automate static testing, static testing technologies can be employed. Following are a few instances: A static testing tool like Source Eter is an example that can help with the analysis of Python, C, C++, Java, and other programming languages' code. Other static testing tools like PMD or Find Bugs can be integrated with it as well.Number of residents in a certain area with wingspan measurements larger than 10 inches = =30% = 0.30
[tex]$=p_o=30 \%=0.30$[/tex]
20 of the 80 bats in a n=80 random sample from outside the area have wingspan measurements larger than 10 inches to ascertain whether there is any variation in the proportion of bats with a wing span more than 10 inches that live outside the region and those that do.
In response to the query;
an investigation using a one-sample z-test,
The following definition applies to the hypothesis:
[tex]$p=\frac{x}{n}$[/tex]
[tex]$p=\frac{20}{80}$[/tex]
H0: The fraction of bats with a wingspan larger than 10 inches that reside outside of the region and those that do so are equal.
= p - p₀ = 0.
Ha! There is a discrepancy between the percentage of bats with a wingspan larger than 10 inches that reside outside of the region and those that do.
= p - p₀ ≠ 0.
n = 80 , X = 20 , p₀ = 0.30
The analysis will be conducted using the z-test for a single proportion.
Following is a sample of the percentage of bats residing outside the area whose wingspan is larger than 10 inches:
The test statistic is,
[tex]& z=\frac{p-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}} \\[/tex]
[tex]& z=\frac{0.25-0.30}{\sqrt{\frac{0.30(1-0.30)}{80}}}[/tex]
The correct test statistic is
[tex]$=\frac{0.30-0.25}{\sqrt{\frac{0.30 \times 0.70)}{80}}}$[/tex]
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Kristin is the manager of a local bank where there are currently 6,700 checking accounts. She wants to collect a sample of checking accounts in order to compile information about customer behavior at the bank. Several different sampling scenarios are described below. Identify the type of sample used in each scenario. Choose from:A. Simple random sample (SRS)B. Stratified sampleC. Cluster sampleD. Systematic sampleE. Convenience sample
Selecting elements from an ordered sampling frame is a statistical approach used in survey methodology known as systematic sampling and in the given situation (D) systematic sampling would be the best.
What is a Systematic sample?Systematic sampling is a statistical technique used in survey methodology that involves choosing components from an ordered sampling frame.
An equiprobability approach is the most typical type of systematic sampling.
This method treats the list's evolution in a cyclical manner, returning to the top after it has been completed.
The sampling process begins with the random selection of one element from the list, followed by the selection of every kth element in the frame, where k is the sampling interval, also known as the skip, and is equal to:
k = N/n.
Therefore, in the given situation (D) systematic sampling would be the best.
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the sampling distribution of the sample mean based on samples of size 2 for the population was simulated, and a histogram of the results was produced. whifh of the following histograms is most likely the histogram of the sampling distribution
The sampling distribution of the sample mean based on samples of size 2 for a population can be approximated by a normal distribution.
The histogram of the sampling distribution would therefore look like a bell-shaped curve. The mean of the sampling distribution is equal to the population mean, and the standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size (in this case, 2).
Therefore, the formula for the sampling distribution of the sample mean for a population of size 2 is:
Mean = Population Mean
Standard Deviation = Population Standard Deviation / √2
The histogram of the sampling distribution would look like a bell-shaped curve with the mean and standard deviation determined by the formula above.
Therefore, the histogram most likely representing the sampling distribution of the sample mean based on samples of size 2 for the population is a bell-shaped curve with the mean and standard deviation determined by the formula above.
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a new restaurant is interested in determining the best time-temperature combination for roasting a five-pound cut of lamb. the times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees fahrenheit and 425 degrees fahrenheit for each time, with the exception of the 90 minute - 425 degree combination. that combination is being eliminated because it will overcook the lamb, which leaves five combinations remaining. from 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. the quality of the finished product is evaluated for each roast. which of the following is true?
The two cuts that are being roasted for each time-temperature combination are an example of replication.
Option (c) is correct.
What is temperature?
Temperature is a measure of the average thermal energy of the particles in a substance. It is a scalar quantity, meaning it has only a magnitude and not a direction. The most commonly used unit of temperature measurement is the degree Celsius (°C) or the degree Fahrenheit (°F), but it can also be measured in Kelvin (K) in scientific and engineering applications.
Given options are:
(a) The two cuts that are being roasted for each time-temperature combination are an example of conduction
(b) The two cuts that are being roasted for each time-temperature combination are an example of convection
(c) The two cuts that are being roasted for each time-temperature combination are an example of replication
(d) None of the above
(c) The two cuts that are being roasted for each time-temperature combination are an example of replication.
In the question it is given that From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. Here it is an act of copying the exact sahpe size of the lamb in all cuts, which is nothing but replication. Moreover, this replication can help in proper comparision.
Hence, The two cuts that are being roasted for each time-temperature combination are an example of replication.
Option (c) is correct.
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A group of students were asked which club they planned to join.
Club Percent of Students
Garden Club 0.1
Robotics Club 0.2
Technology Club 0.5
Zoology Club 0.2
Compare the probabilities of a randomly selected student joining a club and interpret the likelihood. Choose the statement that is true.
The student will be more unlikely to join the Robotics Club than the Garden Club because P(Robotics) < P(Garden).
The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology).
The student will be more likely to join the Zoology Club than the Robotics Club because P(Zoology) > P(Robotics).
The student will be more likely to join the Garden Club than the Robotics Club because P(Garden) > P(Robotics).
Answer:
The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology). 2nd Option B
Step-by-step explanation: I saw it in another one so id like to help
Given the following table of values for a one-to-one function g^-1(x), determine the graph of g(x). X 3 4 6 10 18 g^-1(x) 0 1/2 1 3/2 2
The plot inverse function g^-1(x) is attached below.
What is inverse function?
A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1
Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.
X 3 4 6 10 18
g^-1(x) 0 1/2 1 3/2 2
In the given table x and g^-1(x) is shown.
Hence, THe plot inverse function g^-1(x) is attached below.
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The picture shows two ladders propped against
facing walls. The end of the first ladder is 5m
above the base of the second wall. The second
ladder is 5m above the base of the first wall.
5m
Can you work out at what height the
ladders cross?
Are you surprised that we don't need to know
the distance between the two walls?
5m
5m
10m
This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
What is equal angles ?
Equal angles can be defined as the angles which are equal .
Given ,
The picture shows two ladders propped against facing walls. The end of the first ladder is 5m above the base of the second wall. The second
ladder is 5m above the base of the first wall.
the angles ∠BAD and ∠ADC are alternate angles, and therefore equal. Likewise, angles ∠ABC and BCD are also alternate and therefore equal.
∠BEA and ∠CED are opposite, which means that they are equal. You can see these equal angles in the diagram on the right.
This means that the triangles ABE and DCE have the same angles as each other, and are therefore similar.
so,
This means:
AE/ED=AB/DC=5m/10m=1/2
Therefore AE=1/3 AD.
This means E is 1/3 of the way up from the floor to D, so is at a height of
This means E is 13 of the way up from the floor to D, so is at a height of 10m/ 3=3 1/3m
If instead B is a metres above the floor, then:
AE/ED=AB/DC=a/10
Therefore AE=a/10+a AD.
This means E is the same fraction of the 10m above the floor, so is 10a/10+a metres above the floor.
If instead D is b metres above the floor, then:
AE/ED=AB/DC=a/b
Therefore AE=a/a+b AD.
This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
Therefore, This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
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A principal of $5000 is invested in an account paying an annual rate of 7%. Find the amount in the account after 6 years if the account is compounded semiannually,quarterly, and monthly
The amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly is 6724.4, 6736.7, and 6664.9.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Here, we have
Given: A principal of $5000 is invested in an account paying an annual rate of 7%.
We have to find the amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly.
A) Compounded semi-annually:
= 5000*(1 + 0.05/2)^(2*6) = 6724.4
B) Compounded quarterly:
= 5000*(1 + 0.05/4)^(4*6) = 6736.7
C) Compounded monthly:
= 5000*(1 + 0.05/12)^(12*6) = 6664.9
Hence, the amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly is 6724.4, 6736.7, and 6664.9.
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please help due tn!!
Answer:
Step-by-step explanation:
Answer:
244.5
Step-by-step explanation:
Use A Budgeting Calc This Anwser Is Correct
Find the y-intercept and the x-Intercept of the line below. Click on "None" If applicable.
(a) y-intercept:
(b) x-Intercept:
The x-intercept of the line is (-1, 0). And the y-intercept of the line is not there.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the line is parallel to the y-axis, then the equation of the line parallel to the y-axis will be given as,
x = c
From the equation, the line is passing through (-1, 0), then we have
- 1 = c
c = - 1
Then the equation of the line is x = -1. Then the x-intercept of the line is (-1, 0). And the y-intercept of the line is not there.
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refer to exhibit 26-5. the data illustrate that the firm in question is a group of answer choices price taker (perfectly competitive firm). factor price taker. price searcher (monopolist, oligopolist, etc.). factor price searcher.
According to the given data, the firm in question must be a price-taker, which is a perfectly competitive firm.
A price-taker is basically an individual or a particular company that must accept prices that are prevailing in a market and lacks the market share to be able to influence the market price on its own. All the economic participants can be considered to be price-takers in a market consisting of perfect competition.
In the given data set, the marginal revenue is constant which is very typical for competitive firms. This happens because the market decides the optimal price level and companies do not have much say over the price. This is a way by which they can maximize profits.
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1.
6х6х7х7x7x7
Write using exponents
2.
-104 x -104 x -104
Write using exponents
According to the solving the exponential form of the given number is as follows:
= 6² × 7⁴
= (-104)³
How Do I Write a Formula in Exponential Form?Bases and powers are employed in the exponential form to write numbers. It informs us of the amount of times we must actually multiply a number in order to obtain the answer. When we write the number 125 as 53, for instance, we can see that it is the third power of 5, or the number 125, which looks to be a typical three-digit number when observed.
What does exponential form mean?When a single integer is multiplied by itself a certain number of times, x, the equation y takes on the base component b to the power of x, which is the quantity being multiplied, and is known as the exponential form.
According to the given information:The exponential form of the given number is :
= 6х6х7х7x7x7
= 6² × 7⁴
The exponential form of the given number is :
= -104 x -104 x -104
= (-104)³
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Explain how the commutative property is applied when finding GCF using factor trees
Answer: The commutative property is applied when finding the GCF by taking the factor that has more than 1 factor other than itself(composite) and multiply them until you can no longer multiply. You then take the factors that are in common and multiply them.
Step-by-step explanation: my teacher made me use this way.
On a 800km trip, Ryan's family travelled at 90km/h for the first 600km and 100km/h for
the remainder of the journey. If they had travelled 90km/h for the entire journey, how
much longer would the trip have taken?
The trip would have taken 8.89 hours instead of 8 hours.
How to calculate distance traveled?Distance traveled can be calculated by multiplying the speed at which the object is traveling by the amount of time the object has been in motion.
For example, if a car is traveling at 60 miles per hour for two hours, the distance traveled would be 120 miles.
To calculate distance more accurately, you can use the formula d = rt, where d is the distance, r is the rate of speed, and t is the time in which the object has been in motion.
It is important to note that this formula assumes a constant speed throughout the duration of the journey.
It is also important to remember that the unit of measurement used for both the speed and the time must be the same. Therefore, if the speed is in miles per hour, the time must also be in hours.
In order to calculate this, we need to first calculate the time it took for the family to travel the first 600km at 90km/h. This can be calculated using the formula:
Time = Distance / Speed
So, the time it took for the family to travel the first 600km is:
Time = 600km / 90km/h = 6.67 hours
Then, we can calculate the time it would have taken for the family to travel 800km at 90km/h using the same formula:
Time = 800km / 90km/h = 8.89 hours
Therefore, the trip would have taken 8.89 hours, which is 0.89 hours longer than the original trip which took 8 hours.
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a father is now four times as old as his son. five years ago, he was exactly one and a half times as old as his son ten years from now. find the sum of their present ages
Answer:
sum of their present ages is 5 + 20 = 25 years.
Step-by-step explanation:
The father's current age is 4x (because he is four times as old as his son)
Five years ago, the father's age was (4x - 5) and the son's age was (x - 5)
Ten years from now, the father's age will be (4x + 10) and the son's age will be (x + 10)
From the second statement, we know that:
(4x - 5) = 1.5(x - 5)
And from the third statement, we know that:
(4x + 10) = 1.5(x + 10)
We can solve these equations simultaneously to find the present ages of the father and the son.
Solving the first equation:
4x - 5 = 1.5x - 7.5
2.5x = 12.5
x = 5
So the son's current age is 5 years old.
The father's current age is 4x = 4(5) = 20 years old.
So, the sum of their present ages is 5 + 20 = 25 years.
Need help please help
Answer:
[tex]\frac{7d}{15}[/tex]
Step-by-step explanation:
Is d = 6 a solution to the inequality below?
13 < d + 3
Answer:
Step-by-step explanation:
d = 6 would not be a solution to the inequality below because it would make the inequality untrue! Plugging in, we get:
13 < d + 3
13 < 6 + 3
13 < 9
We know that 9 is not a solution to the inequality!
To solve, we isolate the d, and from there we can find all values that are a solution to the inequality to the solution!
[tex]13 < d + 3\\\\13 - 3 < d\\\\10 < d[/tex]
Thus, one can say that the solutions to the inequality are: [R, d > 10]!
