what is x in the equation :
[tex]8(x - 5/2) = 3x[/tex]
Answer:
x = 4
Step-by-step explanation:
8(x - [tex]\frac{5}{2}[/tex] ) = 3x ← distribute the parenthesis by 8
8x - 20 = 3x ( subtract 3x from both sides )
5x - 20 = 0 ( add 20 to both sides )
5x = 20 ( divide both sides by 5 )
x = 4
Two consecutive Integers have a sum of 67. Find the Integers.
Answer:
33, 34
Step-by-step explanation:
we must start solving this equation by letting a variable equal the smaller number
let n = smaller number
now the larger number is consecutive so you add one to n to get it
n + 1 is the bigger number
if you add them you get 67
n + n + 1 = 67
now solve
add like terms
2n + 1 = 67
subtract 1 from both sides
2n = 66
n = 33
the smaller number is 33
adding one to that will get you the larger integer
33 + 1 = 34
that is the larger integer
Question 6 - (4 marks available) Sanjit drives the 45 km distance between York and Leeds. He then drives a further 42 km from Leeds to Blackpool. Sanjit's average speed between York and Leeds was 54 km/h. It also took Sanjit 35 minutes to travel from Leeds to Blackpool. Work out Sanjit's average speed (in km/h) for his total journey from York to Blackpool.
Answer:
58,5km/h
Step-by-step explanation:
Vyork-leeds=45km/h
Vleeds-blackpool=72km/h
(45+72):2=58,5km/h
PLS HELP ASAP!!!!!!
Are lines L1 and L2 Parallel? Are lines L1 and L4 perpendicular? Explain your thinking.
answer
Calculate the slopes of the 2 lines and compare them.
m = (y2 - y1)/(x2 - x1)
If they are equal, the lines are parallel. If one slope is the negative reciprocal of the other, the lines are perpendicular. If neither of these conditions are met, the lines are not parallel and are not perpendicular. You have all the information you need. Do the math.
Step-by-step explanation:
hope it helps
5. The half-life of a certain radioactive material is 78 hours. An initial amount of the material has
a mass of 790 kg. Write an exponential function that models the decay of this material. Find
how much radioactive material remains after 18 hours. Round your
answer to the nearest
thousandth.
Answer:
395 = 790e^(k*78)
Step-by-step explanation:
Dividing by 790 and taking the natural log
ln ( 395/790 ) = ( kx78 )
-0.6931 = 78k
-0.00888 = k
Now calculate how much is left after 18 hours:
Amount ( 18 )
= 790e^( -0.00888x18 )
Amount = 673.301 kg
a chart in which the data is arranged in vertical columns and that is useful for showing data changes over time or comparisons among items. False or True
The answer to the given question is true. A chart where the data is arranged in vertical columns is called Column Chart, and this chart is useful for showing data changes over time or illustrating comparisons among items.
What is column chart?
Column chart is a type of chart that compares different object levels over time using a vertical format. It is a chart in which the data is arranged in columns and this is useful for showing data changes over a period of time or for illustrating comparisons among items.
Data that is arranged in columns or rows on a worksheet can be plotted in a column chart. In column charts, categories are typically organized along the horizontal axis and values along the vertical axis. Column charts are useful to show how data changes over time or to show comparisons among items.
Column charts are not useful when there are a lot of categories. Catagories organized along the x-axis, while numbers or numerical values ligned in the y-axis.
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The given lengths are two sides of a right triangle. All three sides of the triangle form a Pythagorean Triple. Find the length of the third side and tell whether it is a leg or the hypotenuse. 9 and 41
Answer:
40, leg
Step-by-step explanation:
The triangle has side lengths of 9, 40, and 41.
41 is the hypotenuse, so 40 is a leg.
Morning knows that 15 pounds of hamburger meat will make 60 hamburgers. If Morgan needs to make 100 hamburgers for the picnic. How much hamburger meat does she need to buy?
?
Answer:
25 pounds of hamburger meat
Step-by-step explanation:
you need 15 pounds for 60 hamburgers.
We can turn this into a fraction.
15/60
now we need to make the denominator a power of ten.
15/60
=5/20
=25/100
She needs 25 pounds of hamburger meat
Margin of error: 0.007, confidence level 94%
The minimum sample size required for a 94% confidence interval with a margin of error of 0.007, using the z-distribution, is of:
18,033.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds obtained by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are presented and explained as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 94%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.94}{2} = 0.97[/tex], so the critical value is z = 1.88.
We have no estimate of the population proportion, hence we consider [tex]\pi = 0.5[/tex], which is when the largest sample size is required.
The margin of error is of M = 0.007, hence the sample size required is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.007 = 1.88\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.007\sqrt{n} = 1.88 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{1.88 \times 0.5}{0.007}[/tex]
[tex](\sqrt{n}) = \left(\frac{1.88 \times 0.5}{0.007}\right)^2[/tex]
n = 18,033.
The sample size was rounded up, as a sample size of 18,032 would result in a margin of error slightly above the desired 0.007.
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Carrie sent 190 total text messages in the first five days of May. How many text messages would she send by the end of that month if the rate stayed the same?
Step-by-step explanation:
190 = 5
? = 30
30 / 5 = 6
190 x 6 = 1140
If a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d=3.57√/h. Suppose the person's eye level is 5.76 meters
above sea level. How far can she see to the horizon?
Round your answer to the nearest tenth.
kilometers
She can see the horizon till 2.604 meters when the person is standing at a height of 5.76 meters above sea level.
Given that,
If a person can see d kilometers into the distance from her eye level, which is h meters above sea level, then d=3.57 √h. Let's say the person is standing at a height of 5.76 meters above sea level.
We have to find she can see the horizon, but how far.
The SI unit of length is the meter. In addition to meters, length can also be expressed in other units like centimeters, inches, feet, and yards.
So,
d=h
3.57 √h= 5.76 meters
Divide both sides by 3.57
√h= 5.76 meter/ 3.57
√h=1.614
Squaring on both sides.
h=2.604
Therefore, She can see the horizon till 2.604 meters when the person is standing at a height of 5.76 meters above sea level.
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You use a pair of shoes to measure a distance. The shoes are 12 inches long. The distance is equal to the length of 21 of the shoes. What is the distance? i need help pls
The distance is 252 inches.
What is distance?
The distance between two points is the length of a straight line segment that links them. The distance of a point from a line is the length of the shortest line segment from the point to the line.
Given
the length of shoes = 12 inch
The distance is equal to length of 21 of the shoes.
The total distance = 12×21
=252 inch
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Q21.
A delivery company has a total of 160 cars and vans.
the number of cars: the number of vans = 3:7
Each car and each van uses electricity or diesel or petrol.
of the cars use electricity.
25% of the cars use diesel.
The rest of the cars use petrol.
Work out the number of cars that use petrol.
You must show all your working.
30 cars of the delivery company use petrol.
According to the question,
We have the following information:
A delivery company has a total of 160 cars and vans.
The number of cars: the number of vans = 3:7
1/8 of the cars use electricity.
25% of the cars use diesel and rest use petrol.
Let's take the number of cars to be 3x and the number of vans to be 7x.
3x+7x = 160
10x = 160
x = 160/10
x = 16
Number of cars = 3*16
Number of cars = 48
Now, cars that use electricity:
1*48/8
6 cars
Cars that use diesel:
25*48/100
12 cars
Cars that use petrol:
Total number of cars-(number of cars that use electricity and diesel)
48-(6+12)
48-18
30 cars
Hence, 30 cars of the delivery company use petrol.
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Lily has 16 hats. She has 80% as many hats as Miguel. How many hats does Miguel have?
Topic 6: Writing Linear Equations
26. Write a linear equation that passes through
the point (-6, 1) with a slope of 1/2
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-6)}) \implies y -1= \cfrac{1}{2} (x +6) \\\\\\ y-1=\cfrac{1}{2}x+3\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x+4 \end{array}}[/tex]
Frequency of radiation with a wave length of 5.2 cm. (change to meters first)
Frequency of radiation with a wave length of 5.2 cm is 57.7x[tex]10^{8}[/tex]
What is frequency?The number of waves that pass a fixed point in unit time.
Given that, a frequency with a wave length of 5.2 cm
5.2 cm = 0.052 m
Frequency = f = c/λ
f = 3x[tex]10^{8}[/tex]/0.052 = 57.7x[tex]10^{8}[/tex] Hz
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help please..................................................................................................
Answer:
with what
Step-by-step explanation:
lol
where is the picture..................x1000000000000000000
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms. Which ones should he check? 3x and x and 0.5 4 ✔ -m and 8m ✓ -xy² and 2xy² * y and y² * 4xy and -5x²y * m and n ✔ -7 and 6
the answers are 1,2,3,4,8 i just took it rn
From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²; –7 and 6 are the like terms combinations
Like and unlike terms in algebraic expression:In algebraic terms, the terms that contain the same variable and the same power or degree are called like terms, In algebraic like terms, the numerical coefficients can vary but are not variables.
Here are some examples of like terms and unlike terms,
4x and 9x are like terms
3x²y and 10x²y are like terms
2xy and 10yx are like terms
3x and 19y are unlike terms [ ∵ variable is different ]
2xyz and 2xy are unlike terms [ ∵ variables is missing in 2nd term ]
Here we have a set of algebraic terms that can be classified as given below
=> 3x and x - like terms
=> 1/4 and 0.5 - like terms
=> –m and 8m - like terms
=> –xy² and 2xy² - like terms
=> y and y² - unlike terms [ ∵ powers are not same ]
=> 4xy and –5x²y - unlike term [ ∵ powers are not same ]
=> m and n - unlike term [ ∵ variables are not same ]
=> –7 and 6 like terms
Therefore,
From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²; –7 and 6 are the like terms combinations
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The complete Question
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms. Which ones should he check? Choose all that apply.
=> 3x and x
=> 1/4 and 0.5
=> –m and 8m
=> –xy² and 2xy²
=> y and y²
=> 4xy and –5x²y
=> m and n
=> –7 and 6
need answer asap
Graph y <1- 3x
[tex]y < -3x+1[/tex]
Graph below:
Jackson is working two summer jobs, making $10 per hour washing cars and $12 per hour landscaping. Last week jackson worked a total of 14 hours and earned a total of $152. Determine the number of hours jackson worked washing cars last week and the number of hours he worked landscaping last week.
The number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours
The payment of car washing per hour = $10
The payment for landscaping = $12
Total number of hours worked = 14 hours
Number of hours worked in car washing = x
Number of hours worked in landscaping = y
Then the first equation will be
x + y = 14
x = 14 - y
Total amount he earned = $152
Next equation will be
10x + 12y = 152
Here we have to use substitution method
10(14-y) + 12y = 152
140 - 10y +12y = 152
140 + 2y = 152
2y = 152 - 140
2y = 12
y = 12/2
y = 6 hours
Then
x = 14 - y
x = 14 -6
x = 8 hours
Hence, the number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours
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A muic video webite receive 5,000 comment on a new ong they releae. The next day, the artit performed the ong on televiion and an additional 1,500 comment where made on the webite. What wa the percent of increae?
the 30% increase is 1,500 comments made on the website.
A music video website received 5,000 comments on a new song they released.
The next day, the artist performed the song on television and an additional 1,500 comments were made on the website.
As we know,
The percentage increase = [(increase value)/(old value)]x100
Divide the increase by the beginning number and multiply by 100 to determine the percentage increase between two numbers:
Increase value = 1500
old value =5000
Percent of increase = (1500/5000)x100
Percent of increase = 0.3x100
Percent of increase = 30%
30% if the next day, the artist performed.
In mathematics, a percentage is various or a ratio expressed as a fragment of one hundred. it is often denoted the use of the percent sign, "%", despite the fact that the abbreviations "pct.", "pct" and sometimes "laptop" is also used. A percent is a dimensionless wide variety; it has no unit of measurement. The calculation of chances is done and taught in special approaches relying on the stipulations and necessities. in this manner, the same old formulas can be acquired with proportions, which saves them from having to remember them. In so-referred to as intellectual arithmetic.
This unfastened percent calculator computes some of the values related to possibilities, consisting of the sharp distinction between two given values. percentages are essentially fractions where the denominator is 100. to reveal that a number is a percentage, we use the percent image (%) besides the range. as instance, if you purchased seventy-five questions proper out of a hundred on a check (seventy-five/100), you would have scored 75%.
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The number of customers in a store on the first day is represented by (6x-3). The number of customers on the second day is represented by (x-1). Write an expression to find how many more customers visited the store on the first day.
The expression to find how many more customers visited the store on the first day is 5x - 2.
What is an expression?It's important to note that an expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the number of customers in a store on the first day is represented by (6x-3) and the number of customers on the second day is represented by (x-1).
The number of more customers will be:
= Customers on first day - Customers on second day
= 6x - 3 - (x - 1)
= 6x - 3 - x + 1
= 5x - 2
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What is the value of tan A?
21. At the gränd opening of a sporting goods store, the store is giving a free (-shirt to every 12th
person who attends. They give a $25 gift card to every 30th person. Which person will get both
a t-shirt and a gift card?
The person at the 300th number will get a t-shirt and a gift card both.
Given, at the grand opening of a sporting goods store, the store is giving a free shirt to every 12th person who attends.
They give a $25 gift card to every 30th person.
We have to find that which person will get both a t-shirt and a gift card.
To find the person who will get both, we have to find the LCM of 12 and 25.
As, the LCM of 12 and 25 is 300
So, the person at the 300th number will get a t-shirt and a gift card both.
Hence, the person at the 300th number will get a t-shirt and a gift card both.
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HELP!
Which value is equivalent to
Answer: B
Step-by-step explanation:
100/9
11.1
11 1/9
The difference between a number and 5 is -11
Answer: n=-6
Step-by-step explanation:
1. Make your equation
n-5=-11
2. Solve for n by adding 5 to both sides
n=-6
Answer:
16
Step-by-step explanation:
1) Break down the question
We are told that the difference between a number a 5 is minus -11
As it is a minus we have to be careful we are using the correct operation required!
2) Figure out the number
As the difference is -11 we would need add 11 to 5 to get the final number
11 + 5 = 163) Check your answer makes sense
It is always best to double check your answer to make sure that your answer is 100% correct!
To do this we just have to work out way backwards.
16 - 11 = 5As we can see we have to minus 11 from 16 to get to 5 meaning our answer is correct and the number is 16!!!
Hope this helps, have a great day!
Devaughn is 13 years older than Sydney. The sum of their ages is 99. What is Sydney's age?
Sydney's age is 43 years.
According to the question,
We have the following information:
Devaughn is 13 years older than Sydney. The sum of their ages is 99.
Let's take the age of Devaughn to be x years and the age of Sydney to be y years.
So, Devaughn's age can be expressed using the following expression:
y = 13+x years
Now, we have the following expression for the sum of their ages:
x+13+x = 99
2x+13 = 99
Moving 13 from the left hand side to right hand side will result in the change of the sign from plus to minus:
2x = 99-13
2x = 86
x = 86/2
x = 43 years
Hence, Sydney's age is 43 years.
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attending the university of houston main campus the bank agrees to give you a loan of 35000 with 2% simple interest over 8 years
As per the given data, loan amount is $35,000 with 2% simple interest for the time period of 8 years then monthly payment is equal to
$422.92.
As given in the question,
Loan amount taken from the bank is equal to $35,000
Simple interest rate is 2%
Time period = 8 years
Total interest paid is equal to
= Loan amount × Interest rate × time period
= 35,000 × 2% × 8
= (35,000 × 2 × 8) / 100
= $5600
Total amount to be paid
= Loan amount + Interest amount
= $35,000 + $ 5,600
= $ 40,600
Monthly payment done based on given interest and time period
= $40,600 / ( 8 × 12 )
= $ 40,600 / 96
= $ 422.92
Therefore, for the given data, loan amount is $35,000 with 2% simple interest for the time period of 8 years then monthly payment is equal to $ 422.92.
The complete question is:
Attending the university of Houston main campus ,the bank agrees to give you a loan of $35,000 with 2% simple interest over 8 years. How much will your monthly payments be?
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A(n)
O element
O subset
O component
O group
is a member of a set.
Answer:
B. Subset
Step-by-step explanation:
A(n) subset is a member of a set
If the interest for 4 years on rupees 350 be Rs 112,find the rate percent. In what time will rupees 800 amount to rupees 1120 at the same rate of interest?
Using Simple Interest formula ,
The rate percent on amount of Rs.300 is 5.5 .
At same rate, R = 5.5 the principle 800 will be Rs1120 in next 7 years .
In first case we have given that ,
principle = Rs.350
time = 4 years
Amount = Rs 1120
simple interest = 1120-350 = Rs.770
let rate of interest be R% .
Using the formul of simple interest
S.I = P×R×t /100
=> 770 = 350×4×R/100
=> R = 5.5 %
In Second case , rate of interest is same as in first case. So,
Amount = Rs. 1120
Principle = Rs. 800
rate of interest (R)= 5.5
Again simple interest formula Used:
Simple Interest = (P × R × T)/100
Simple interest = 1120 - 800 = Rs. 320
Simple Interest = (P × R × T)/100
⇒ 320 = 800×5.5 ×T/100
=> T = 7.27 ~ 7
∴ In the given principle Rs 800 with same rate of interest will be 1120 in 7 next years .
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