Four less than 5 times a number is the same as 26 more than twice the number.Find the number?
Answer:-Let the number =x
Four less than 5 times of the number means the polynomial is (5x-4)26 more than twice the number means the polynomial is (2x+26)Now according to question Both are equalATQ,
[tex]\sf (5x-4)=(2x+26)[/tex]
Open the brackets[tex]{:}\longrightarrow[/tex][tex]\sf 5x-4=2x+26 [/tex]
Now take unknown polynomials to one side and numbers to other side[tex]{:}\longrightarrow[/tex][tex]\sf 5x-2x=26+4 [/tex]
Now simplify[tex]{:}\longrightarrow[/tex][tex]\sf 3x=30 [/tex]
Now interchange sides and get x[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {30}{3}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]{\underline{\boxed{\bf{x=10}}}}[/tex]
[tex]\therefore[/tex][tex]\sf The\:number\:is\: 10.[/tex]
The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 55 records of automobile driver fatalities in a certain county showed that 34 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County? Use α = 0.01. Solve the problem using both the critical region method and the P-value method. Since the sampling distribution of is the normal distribution, you can use critical values from the standard normal distribution (Round any intermediate calculations to at least four decimal places. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.)
Solution :
Population proportion, P = 77%
Sample size is given by n = 55
Sample proportion = [tex]$\frac{x}{n} = \frac{34}{55}= 0.61$[/tex]
Null hypothesis
The population proportion of the fatalities of the drivers that are related to alcohol = 77%
[tex]$H_0 : P = 77$[/tex] %
[tex]$H_0 : P = 0.77$[/tex]
Alternate hypothesis, [tex]$H_a : P < 0.77$[/tex]
Therefore, the test statistics = [tex]$\frac{0.61 - 0.77}{\sqrt{\frac{0.7 \times 0.23}{55}}}$[/tex]
= -3.2
Critical value = -1.64
and the rejection zone : test zone, -1.645
Therefore, we fail rejecting [tex]$H_0$[/tex]
p value 0.0582
rejection zone :: p value , 0.01
So we fail to reject [tex]$H_0$[/tex]
Thus the data does not indicate the population proportion of the drivers fatalities which are related to the alcohols which is less than 77% in the county of Kit Carson.
Alice’s Athletic Arena requires members to pay $20 to join and members must pay $1.50 for each time they come to work out. Roy’s Romper Room requires members to pay $5 to join and members must pay $4 for each time they come to work out. How many visits will it take for the costs to both be the same?
Answer:
6 visits will it take for the costs to be the same
Step-by-step explanation:
The form of the linear relation is y = m x + b, where
m is the rate of changeb is the initial amountAssume that the number of visits is x, and the total cost is y
∵ Alice’s Athletic Arena requires members to pay $20 to join
→ That means there is an initial amount of $20
∴ b = 20
∵ The members must pay $1.50 for each time they come to work out
→ That means there is a cost for every visit (rate of change)
∴ m = 1.5 dollars/visit
∵ The number of visits = x
∵ The total cost is y
→ Form the linear equation for this situation
∴ y = 1.5x + 20 ⇒ (1)
∵ Roy’s Romper Room requires members to pay $5 to join
∴ b = 5
∵ The members must pay $4 for each time they come to work out
∴ m = 4 dollar/visit
→ Form the linear equation for this situation
∴ y = 4x + 5 ⇒ (2)
∵ The costs to both are the same
→ That means, equate the right sides of (1) and (2)
∴ 1.5x + 20 = 4x + 5
→ Subtract 20 from both sides
∴ 1.5x + 20 - 20 = 4x + 5 - 20
∴ 1.5x = 4x - 15
→ Subtract 4x from both sides
∵ 1.5x - 4x = 4x - 4x - 15
∴ -2.5x = -15
→ Divide both sides by -2.5
∴ x = 6
∴ 6 visits will it take for the costs to be the same
Amanda bought 8 shirts for $132. If long sleeve shirts cost $18 and short sleeve shirts cost $12 , how many of each shirt did she buy? The system of equations to solve this would be:
x + y = 8
or
18x + 12y = 132
Answer:
has to be
Step-by-step explanation:
the first one
Answer:
18x = 12y =132
Step-by-step explanation:
I need help with solving this problem please I will mark brainliest if correct !!!
Answer:
x = 20
4x = 80°
5x = 100°
Step-by-step explanation:
The given angles are supplementary so their sum is 180°
4x + 5x = 180
9x = 180 divide both sides by 9
x = 20
The value of the angle marked 4x = 4 × 20 = 80°
The value of the angle marked 5x = 5 × 20 = 100°
Answer:
80°, 100°
Step-by-step explanation:
The 2 angles are same- side interior angles and are supplementary, thus
4x + 5x = 180
9x = 180 ( divide both sides by 9 )
x = 20
Thus
4x = 4 × 20 = 80°
5x = 5 × 20 = 100°
can someone help plz
Answer: 20
Step-by-step explanation:
Write the number three-hundred-sixty-five-thousandths in standard form.
Answer:
365/1,000 or .365
Step-by-step explanation:
HTH :)
Three hundred sixty five thousand in standard form is 365000.
What is standard form and word form of numbers ?The standard form of numbers is when we have to write the number in digits according to it's place and face value.
Word form of numbers is that when we have to write numbers given in numerical form to words by determining place and face value.
According to the given question we have to write three thousand sixty five thousand in standard form.
We know thousand has three zeroes.Suppose we have to write one thousand in standard form which is 1000.
Given we have to write three hundred sixty five thousand in standard form which is 365000.
learn more about numbers here :
https://brainly.com/question/17264364
#SPJ2
a point on a perpendicular bisector is 7cm from each endpoint of the bisected segment and 5cm from the point of intersection. What is the length of the segment?
9514 1404 393
Answer:
about 9.80 cm
Step-by-step explanation:
The length of half the segment (h) can be found from the Pythagorean theorem:
h² +5² = 7²
h² = 7² -5² = 49 -25 = 24
h = √24 = 2√6
This is half the segment length, so the whole segment length is ...
L = 2h = 2(2√6)
L = 4√6 ≈ 9.7980
The length of the segment is 4√6 ≈ 9.80 cm.
Find the value of y
Answer:
y = 11°
Step-by-step explanation:
PR and QS and parallel lines and QR is a transversal.
Now,
5y = 55 (alternate interior angles)
y = 55/5
y = 11
People asked what the Absolute Value Homework looked like so here it is. I appreciate the help!
Answer:
thank you!
Step-by-step explanation:
3. A chessboard is covered by 64 squares that are of the same size.
(a) How many squares fit along the side of the chest board?
b) How many squares fit along the perimeter of the chessboard
2x + 8y = 6
-5x - 20y = -15
Answer:
The total would be 40.53
Or
Solve for the first variable in one of the equations, then substitute the result into the other equation.
x = 3 − 4 y
Step-by-step explanation:
This question is incomplete so
The base of a triangle is 5 meters greater than the height. If the area of the triangle is 102 m2, which are the dimensions of the base and the height?
Answer: The base is 17 meters long, and the height is 12 meters.
Step-by-step explanation:
The area of a triangle is:
A = b*h/2
where:
b = base
h = height.
For this particular triangle, we have that:
b = 5m + h
A = 102 m^2 = b*h/2
We can replace the first equation into the second one:
b*h/2 = 102 m^2
(5m + h)*h/2 = 102 m^2
(5m + h)*h = 2*102 m^2 = 204m^2
5m*h + h^2 = 204m^2
We can rewrite this as a quadratic equation:
h^2 + 5m*h - 204m^2 = 0
The solutions are given by the Bhaskara formula, the solutions are:
[tex]h = \frac{-5m +- \sqrt{(+5m)^2 -4*1*(-204m^2)} }{2*1} = \frac{-5m+-29m}{2}[/tex]
Then the two solutions are:
h = (-5m - 29m)/2 = -17 m
This is a negative height, that is not really defined, so this will be discarded.
The other solution is:
h = (-5m + 29m)/2 = 12m
This is positive, so this is the option we will use.
Knowing h, we can find the value of b.
b = 5m + h = 5m + 12m = 17m
Then the area is:
A = 12m*17m/2 = 102m^2
Help! Show work please
will mark brainliest
Answer:
x = 62.23 ft
y = 47.67 ft
Step-by-step explanation:
It costs $4 to sign up for a music download service and $0.50 to download each song. Jada signs up for the service
and begins downloading music.
1. Complete the table showing how Jada can spend money downloading songs.
Step-by-step explanation:
Note: I could not find any attached table of values, however, we can make do with the information given
step one:
the cost of sign up = $4
the cost of download for each song= $0.5
Step two:
Required
we want to find the cost of downloading any number of songs.
let the number of songs be x
and let the total cost be y
Hence the cost function is
y=0.5x+4
now supposing the value of x which is the number of downloads from the table is 10, then the total cost for 10 downloads will be
y=0.5(10)+4
y=5+4
y=9
Hence it will cost $9 to download 10 songs, just plug in the value of x into the cost function
On Sunday 440 people visited a museum that charges $9 for each child and $12.50 for each adult. If the museum earned $5,220 on that day, how many adults visited the museum on Sunday?
1) (5x - 4)(x - 5) = 0
Answer: The answer is 1.5
Step-by-step explanation: First you want to add 5x + x which equals 6x. Then you want to add -5+-4 which = -9. Then you add 9 to the -9 to get rid of it. But you have to do it on both sides so you add 9+0 which =9. Finally you divide 9 by 6 which equals 1.5
Which of the following is a multiple of 8?
A: 22
B: 48
C: 18
D: 30
Fen completed a triathlon race whose total distance is DDD kilometers. First, she swam a distance of 0.50.50, point, 5 kilometer. Then, she rode a bicycle for xxx hours at an average speed of 202020 kilometers per hour. Finally, she ran for 0.50.50, point, 5 hour at an average speed of vvv kilometers per hour. Write an equation that relates DDD, xxx, and vvv.
Answer:
D = 0.5 + 20x + 0.5v
Step-by-step explanation:
Initial distance covered d1 = 0.5km
If she rode a bicycle for x hours at an average speed of 20 kilometers per hour, then her distance during thus period is,;
Speed = Distance/Time
Distance d2 = speed × time
d2 = 20x
If she ran for 0.5 hour at an average speed of v kilometers per hour, her distance this time will be;
Distance d3 = 0.5v
If her total distance is D, then;
D = d1+d2+d3
D = 0.5 + 20x + 0.5v
Hence an equation that relates D, x, and v is D = 0.5 + 20x + 0.5v
Over what axis was the square reflected in the first example?
Answer:
theres no picture attached
Step-by-step explanation:
find the ratio if it is given that,
a+3b/5= a-2b/[tex]a+3b/5= a-2b/2[/tex]2
Answer:
dbhjnhygtfvbhnj
Step-by-step explanation:
Given the congruency statement, list all congruent angles and sides
Answer:
Angles: ∠ABC ∠BAC ∠ACB ∠CBA ∠CAB ∠BCA ∠A ∠B ∠C
Sides: AB BA AC CA CB BC
The line is suppose to go over the sides indicating its a segment but I couldn't find the symbol for that
Step-by-step explanation:
what number decreased by 3.5 equals 12.7 i have to write an equation then solve the problem
Answer:
n - 3.5 = 12.7
n=16.2
Step-by-step explanation:
n - 3.5 = 12.7, to solve add 3.5 to both sides
n = 12.7 + 3.5
n=16.2
Can someone help me answer this question plz and thank you
I think it's a or d. Forgive me if I am wrong :(
Answer:
The equation has a greater slope.
Step-by-step explanation:
The slope of the equation is 4 while the slope of the table is 3 because y increases 3 every time x increases 1.
Create an equation to represent the following situation: I am selling rings for $2 and pins for $1. I want to make $40. Let x represent the number of rings and y represent the number of pins. (SOMEONE HELP PLEASE)
If a 4 ft. pole casts a 5 ft shadow, how high is a pole that casts a 15 ft shadow? 1
Answer:
12 ft!!
Step-by-step explanation:
can u pls mark me brainliest?
Answer:
x=12 ft
Step-by-step explanation:
4/5=x/15
Multiply 5 and x to get 5x, then multiply 4 and 15 to get 60, then you're left with the equation 5x=60. Divide both sides of the equation by five to get 12 :D.
Using the greatest common factor for the terms, how can you write 32 + 24 as a product?
Answer:
25
Step-by-step explanation:
bob buys a t-shirt for $7.45 he pays with a 20 bill. how much change will he get?
im in 5 grade im 10 years old can you solve this for me please
Answer:
$12.55
Step-by-step explanation:
Subtract! 20 - 7.45
wy
3.2
Starnes
GPA SAT-M
2.9
670
2.86
520
2.6
570
3.6
710
600
2.7
590
640
3.085 570
3.75
710
3.4
630
3.338 630
3.56
670
3.8
650
3.2
660
510
3.1
McGrail
GPA SAT-M
2.9
620
3.3
590
3.98
650
2.9
600
3.2
620
3.5
680
2.8
500
2.9
502.5
3.95
640
3.1
630
2.85
580
2.9
590
3.245 600
3.0
3.0
620
2.8
580
2.9
600
600
600
3.1
3.2
Was the class stacked
Answer:
Starnes 2.9
Step-by-step explanation:
-6x + 8y = 24
What is the answer?
Answer:
x=-4 y=3
Step-by-step explanation:
this is what the girl said in the comment section :) so i plugged them into the equation and she was right
please help, todays the last day
Answer:
b
Step-by-step explanation:
fiber hard to digest i love you