Answer:
Since [tex]f(0) < f(x) < f(1)[/tex], there is a solution for [tex]f(x)[/tex] between [tex]x = 0[/tex] and [tex]x = 1[/tex].
Step-by-step explanation:
A solution of the polynomial is a root such that sign of dependent value changes, either from positive to negative or from negative to positive. Let [tex]f(x) = x^{3} + 6\cdot x - 5[/tex], [tex]x[/tex] is a solution of the equation if and only if [tex]f(x) = 0[/tex]. We proceed to evaluate the function at each bound:
x = 0
[tex]f(0) = 0^{3}+6\cdot (0) - 5[/tex]
[tex]f(0) = -5[/tex]
x = 1
[tex]f(1) = 1^{3}+6\cdot (1) - 5[/tex]
[tex]f(1) = 2[/tex]
Since [tex]f(0) < f(x) < f(1)[/tex], there is a solution for [tex]f(x)[/tex] between [tex]x = 0[/tex] and [tex]x = 1[/tex].
Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $65 per hour. The mechanics
combined total of 15 hours, and together they charged a total of $1475. How long did each mechanic work?
Answer:
Here is another case where we have two unknowns (the number of hours each mechanic worked) so we'll need two equations to solve.
Let A = number of hours first mechanic worked (the one who charged $45/hour)
Let B = number of hours second mechanic worked (the one who charged $105/hour)
From the problem statement, we know that the two mechanics worked a combined 35 hours so the first equation is:
Equation 1: A hours + B hours = 35 hours
We also know that in total, the charge was $2475. So the second equation is:
Equation 2: (A hours x 45 dollars/hour) + (B hours x 105 dollars/hour) = 2475 dollars
So our two equations are:
1: A + B = 35
2: 45A + 105B = 2475
Multiply both sides of the first equation by -45 to get the following:
-45A - 45B = -1575
Now the two equations are:
1: -45A - 45B = -1575
2: 45A + 105B = 2475
Add them together and the "A" term drops out:
-45B + 105B = -1575 + 2475
or
60B = 900
Now divide both sides by 60:
B = 15
Now plug B = 15 into the first equation:
A + 15 = 35 thus A = 20
So Mechanic A (at $45/hour) worked 20 hours and Mechanic B (at $105/hour) worked 15 hours
Check: 20x45 + 15x105 = 900 + 1575 = 2475
Step-by-step explanation:
hope it helps you (:
tan 2A + sin 2A=4 tan A/(1 - tan4 A)
Answer:
[tex]when \: \\ \tan(2x) = \frac{2 \tan(x) }{1 - {( \tan(x)) }^{2} } \: \: and \\ \sin(2x) = \frac{2 \tan(x) }{1 + {( \tan(x)) }^{2} } \\ then \\ \sin(2x) + \tan(2x) = \frac{2 \tan(x) }{1 - {( \tan(x)) }^{2} } + \frac{2 \tan(x) }{1 + {( \tan(x)) }^{2} } \\ = \frac{2 \tan(x)(1 + {( \tan(x)) }^{2} + 2 \tan(x) (1 - {( \tan(x)) }^{2} }{(1 + {( \ \tan(x)) }^{2}(1 - {( \tan(x)) }^{2} } \\ = \frac{2 \tan(x) \times 2 }{1 - {( \tan(x) }^{4} } \\ = \frac{4 \tan(x) }{1 - {( \tan( \times ) )}^{4} } [/tex]
Step-by-step explanation:
If you need any explanation. I can do it, my friend. you can communicate with me to that or any thing do you need in math
Ben has $19 to spend. He spent $7.25, including tax, to buy a notebook. He needs to save $2.75 but he wants to buy a snack. If pretzels cost $0.50 per package including tax, what inequality would show the maximum number of packages that Ben can buy?
PLS HELP ASAP:
- what is the INEQUALITY FOR THIS PROBLEM. THAT'S ALL IM ASKING. DON'T SOLVE IT.
Answer:
($19 - $7.25) - $2.75 ÷ (0.50p) ≤ 19
Step-by-step explanation:
First, let's define the variable:
p = pretzel packages
Let's first find out how much money Ben has after buying the notebook.
$19 - $7.25 = $11.75
So, we know that Ben has $11.75 left.
The inequality would be: ($19 - $7.25) - $2.75 ÷ (0.50p) ≤ 19
A car is parked 80 feet from the base of a 120-foot building. What is the angle of depression from the top of the building to the car? Round your answer to the nearest degree.
A 48° degrees
B 34° degrees
C 42° degrees
D 56° degrees
0.5(400 + d) =4.25 d=
Answer:
d = 53.33333
Step-by-step explanation:
Solve for d on calculator
Answer:
pleas help me asap please!!!!!!
pleas help me asap please!!!!!!
Step-by-step explanation:
pleas help me asap please!!!!!!
Suppose I randomly choose 4 distinct integers between 1 and 60. Is it true, or is it not true, that at least 2 of them must differ by no more than 19.
Answer:
It’s true
Step-by-step explanation:
Proof by induction
Let the four chosen numbers be x_1, … x_4 and, without loss of generality, let x_1 < x_2, … < x_4.
For x_1 = 1, the smallest possible choice, let x_2 = x_1 + 20 = 21 be the smallest possible choice that has a difference larger than 19. Likewise, x_3 = x_2 + 20 = x_1 + 40 = 41. Then x_4 has to be at least x_3 + 20 = x_1 + 60 = 61 which is out of range.
For the induction, suppose that x_4(n) = x_1(n) + 60 > 60 and therefore x_4(n) can’t be chosen for a given x_1(n). Then incrementing x_1(n+1) = x_1(n) + 1 would require x_4(n+1) to be at least x_1(n) + 1 + 60 = x_4(n) + 1 > 61, so this is out of range as well.
For another induction, suppose that x_4(n) = x_2(n) + 40 > 60 and therefore x_4(n) can’t be chosen for a given x_2(n). Then incrementing x_2(n+1) = x_2(n) + 1 would require x_4(n+1) to be at least x_2(n+1) + 40 = x_4(n) + 1 > 61, so this is out of range as well.
Likewise, for the induction, suppose that x_4(n) = x_3(n) + 20 > 60 and therefore x_4(n) can’t be chosen for a given x_3(n). Then incrementing x_3(n+1) = x_3(n) + 1 would require x_4(n+1) to be at least x_3(n+1) + 20 = x_4(n) + 1 > 61, so this is out of range as well.
Therefore all choices of x_1, x_2, x_3 with differences greater than 19 leaves no choice of x_4 within range with x_4 > x_3 + 19.
How many times bigger is a group of 21 marbles than a group of 7 marbles?
Answer:
21/7=3
3 times bigger.
Step-by-step explanation:
5r + 2(3r - 1) = -46
please show the work
Answer:
R = - 4
Step-by-step explanation:
5 r + 6r - 2 = - 46
11 r - 2 = - 46
11 r = - 46 + 2
11 r = - 44
r = - 4
Ivan and Tanya share £150 in the ratio 4: 1
Work out how much more Ivan gets compared to Tanya.
Answer:
Ivan got £90 more than Tanya.
Step-by-step explanation:
Ivan and Tanya share the amount £150 in the ratio of 4 : 1
Amount received by Ivan = [tex]150\times \frac{4}{(4+1)}[/tex]
= [tex]150\times \frac{4}{5}[/tex]
= £120
Similarly, amount received by Tanya = [tex]150\times \frac{1}{(4+1)}[/tex]
= £30
Difference in their amounts = 120 - 30
= £90
Therefore, Ivan got £90 more than Tanya.
21/5 as a whole number
M<6=(x+10), m<2=(x+15)
<6 and <2 are alternate interior angles
Answer:
ano ang pinag kaiba noon kaysa ngayon
(1/2x-3/8) ÷1/3+4/7(5-1/4x)
Answer:
[tex]\frac{19}{14}x + \frac{97}{56}[/tex]
Step-by-step explanation:
I've written my working in the picture. I hope it's clear. :,)
I've expanded the brackets, simplied the fractions before simplifying them again, having found the common denominators of the constants and x terms.
Find C and a so that f(x) = CaX models the situation described. State what the variable x represents in your formula. In 2000 a house was worth $220,000, and its value decreases by 11% each year thereafter. please help im failing
Answer:
f(x) = Ca^x
x = years since 2000.
f(0) = 220000 = Ca^0 = C
f(x) = 220000a^x
f(1) = 220000(1-0.11) = 220000a^1
a = 0.89
f(x) = 220000(0.89)^x
So each year reduces by 89%
What is the circumference of this circle?
Answer:
37.68
Step-by-step explanation:
[tex]c = 2 \times 6 \times 3.14 = 37.68[/tex]
Please I need help fast please help me
Answer: 0-o uhhhh 0-o
uhhhh0-o
Step-by-step explanation:
¿conjunto de fuerzas aplicado sobre un objeto de manera que la linea de accion de todas las fuerzas convergan en un mismo punto?, ¿ cual es el conjunto de esas fuerzas? . agradecería mucho si lo contestan porfis uwu
Answer:
Fuerzas Convergentes
Fuerza Resultante
Tina went out to eat and her bill was $24.75.
She wants to leave the waiter a 20% tip. How
much more money will be added to her bill
once she included the tip?
Answer:
your awnser should be. 24.75 + 20% = $29.70
so the amount added to her bill is $4.95
Answer:
the bill will be 4.95 more than the original cost without the 20% tip.
Step-by-step explanation:
cost before tip: 4.75
cost after 20% tip: 29.70 or 30.00 (rounded)
Enter the value of (−8)(45)(18).
Jackson practices piano four times a week he practices for 40 minutes each time how many minutes does Jackson practice until weeks
Answer:
160 min or 2.66666667 hours per a week
Step-by-step explanation:
its very simple
40*4=160
hope I helped :)
The ratio of boys to girls in a class is 2 to 3. There are 10 boys in the class. How many girls are there? Be sure to show your work.
Answer:
15 girls
Step-by-step explanation:
Well, the ratio of 2/3, boys to girls. So, you would then try to find an (almost) common denominator, so 2/3 is equivalent to 10/15. In this case, there would be 15 girls
Lol hope this helps
Find each value below.
Answer:
7.) x = 21
8.) y = 6
9.) angle F = 62 degrees
10.) TS = 10
Step-by-step explanation:
5y-2 = 28
5y = 30
y = 6
4x+6 = 90
4x = 84
x = 21
angle F = 90-28
angle F = 62 degrees
3z-8 = z+4
2z = 12
z = 6
TS = z+4 = 10
BRAINLIEST PLS HELP!!!
Question 3
Find the slope-intercept form of the equation of the line that passes through (-6, 2)and is parallel to y=2x+3
Answer:
How to use Algebra to find parallel and perpendicular lines. ... y = mx + b. Slope- Intercept Form ... Find the equation of the line that is: ... For y = 3x + 2: the slope is 3, and y- intercept is 2.
The Large Counts Condition must be met so that the sampling distribution of a sample proportion is approximately normal. Using appropriate notation, write out the Large Counts Condition for Normality.
Answer:
np>10 and n(1-p)>10
Step-by-step explanation:
Appropriate notation the Large Counts Condition for Normality is The Large Counts Condition for Normality states that is the number of successes and failures which should be above the 10 to be assume normality that is here express as n(p)>10 and n(1-p)>10 This is the notation of the Large Counts Condition for Normality.The Large Counts Condition for Normality: np ≥ 10 and nq ≥ 10.
The Large Counts Condition, also known as the Large Sample Size Condition, is a requirement that must be met to ensure that the sampling distribution of a sample proportion is approximately normal when sampling from a population. This condition is necessary to apply the normal distribution to the sample proportion for various statistical inferences.
Let's denote the following:
- n: The sample size, i.e., the number of observations in the sample.
- p: The population proportion of the characteristic of interest.
- q: The complementary probability to p, such that q = 1 - p.
The Large Counts Condition for Normality states:
np ≥ 10 and nq ≥ 10
In other words, the product of the sample size (n) and the population proportion (p) must be greater than or equal to 10, and the product of the sample size (n) and the complementary probability (q) must also be greater than or equal to 10.
When both of these conditions are satisfied, the sampling distribution of the sample proportion can be approximated by a normal distribution. This approximation is useful for constructing confidence intervals and performing hypothesis tests related to proportions.
To know more about Large Counts, refer here:
https://brainly.com/question/30984845
#SPJ6
1 Expand and simplify each expression
a) x(x+2)+x(x+5)
THIS IS FOR AN EXAM NEED HELP!!! Directions: Show all your steps as you solve the following problems. Round the solutions to the nearest hundredth if necessary.
7. On a 40‐point test, Steve received an 80%. How many points did he receive on the test?
8. Of the 8760 hours in a year, most televisions are on for 2190 hours. What percent is this?
9. The population of a town increased from 620 to 700. What is the percent of increase?
10. The population of a small town increased 23% from its population in 2000 to its population in 2003.
If the population of the town in 2000 was 25,314, what was its population in 2003?
11. To control his weight, Joel reduced his calorie intake from 2500 calories to 1950 calories each day. What was his percent of decrease for calorie intake?
12. The sales tax in Whittle City is 7%. How much tax is charged on a purchase of $53?
13. What is the simple interest on $2500 invested at an interest rate of 6% for 2 years?
14. Shawn earned a 5% commission on a $500 sale. How much did he earn?
15. Andrew measured the time it took for an apple to fall 50 feet as 1.95 seconds, but his calculations show that it should be 1.77 seconds. What was his experimental error?
1. 32 points 2. 25% 3. 2,100 4. 22% 5. 56.71 6. $300 7. $25 8. The answer for given problem is -2, but Andrew get -21.6 which is wrong.
Step-by-step explanation: brainliest pls ^^
Help i need to finish it today And can you explain the steps so i wont need help next time or if you don’t want to its okay :)
Answer:
110 feet
Step-by-step explanation:
The formula to find the area of a rectangular prism is A = 2 (wl + hl + hw)
Substitute the values:
A = 2 (5x5 + 3x5 + 3x5)
A = 2 (25 + 15 + 15)
A = 2 (25 + 15 + 15)
A = 2 (55)
A = 110
hey! please help on this question i'll give brainliest <333 .
Answer:
C, the third choice
Step-by-step explanation:
Anthony's little brother gets on a carousel that is 8 meters in diameter. At the start of the ride, his brother is 3 meters from the fence to the ride. How far will his brother be from the fence after the carousel rotates 240°?
Answer:
9 m
Step-by-step explanation:
Given that:
Carousel diameter = 8m
Radius of carousel = 8m / 2 = 4m
From the attached picture :
xo = d ; from the diagram attached ;
Using Pythagoras :
Cosθ = Adjacent / hypotenus
Cos 60 = d / 4
0.5*4 = d
d = 2
d = 2m
d + length of Radius + initial distance from fence
2m + 4m + 3m = 9m
40 is 20 of what number
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{40 is 20\% of what time number?}\\\\\\\bullet \large\bold{We\ are\ looking\ for\ your\ UNKNOWN\ number; we\ can\ the\ value}\\\large\bold{is\ \underline{a}\ for\ our\ answer!}\\\bullet\large\bold{REMEMBER: Percentages\ are\ out\ 100\ \& the\ word\ \underline{of}\ means\ \underline{multiply}}[/tex]
[tex]\huge\text{NOW LETS SOLVE FOR YOUR ANSWER!}[/tex]
[tex]\bold{Equation: 20\%\ \times \ a\ =\ 40}\\\\\bold{a = \dfrac{40}{20\%}}}\\\\\bold{20\% = \dfrac{20}{100}\rightarrow 0.2}}}\\\\\bold{Equation: a = \dfrac{40}{0.2}}\\\\\bold{\dfrac{40}{0.2}=200}\\\\\bold{a=200}\\\\\boxed{\boxed{\bold{Answer: 200}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]