Therefore, the final answer with two significant digits is:Combined length = 110 cm
The combined length of the two rods can be found by adding the length of the first rod and the length of the second rod. The length of the first rod is given as 31.4 cm and the length of the second rod is given as 82.25 cm. Therefore, the combined length of the two rods can be found as follows:Combined length = length of first rod + length of second rod= 31.4 cm + 82.25 cm= 113.65 cm
However, we need to report our answer with the correct number of significant digits. The least number of significant digits in the given values is two, which is the number of significant digits in 31.4 cm. Therefore, we must round our answer to two significant digits. Since the digit in the hundredth place is 5, which is greater than or equal to 5, we must round up the digit in the tenth place.
To know more about significant digits:
https://brainly.com/question/28993414
#SPJ11
Julia writes 2 fractions with the same denominator that have numerators 8 and 2 . What could the denomination be if the sum is less than 1.?Equal to 1? Greater than 1?
If the sum of the fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.
To find a denominator that satisfies the given conditions, we can consider the fractions with numerators 8 and 2. If the sum of these fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.
To determine the possible denominators that satisfy the conditions, we need to consider the given numerators of 8 and 2. Since the fractions have the same denominator, let's denote it as 'd'. The fractions can be written as 8/d and 2/d.
If the sum of these fractions is less than 1, we have:
8/d + 2/d < 1
Combining the fractions, we get:
(8 + 2)/d < 1
Simplifying, we have:
10/d < 1
To satisfy this inequality, the denominator 'd' can be any number greater than 10. For example, if we choose d = 11, the fractions become 8/11 and 2/11, and their sum is 10/11, which is less than 1.
If the sum of the fractions is equal to 1, we have:
8/d + 2/d = 1
Combining the fractions, we get:
10/d = 1
Solving for 'd', we find that the denominator must be 10. For example, if we choose d = 10, the fractions become 8/10 and 2/10, and their sum is 10/10, which is equal to 1.
If the sum of the fractions is greater than 1, we have:
8/d + 2/d > 1
Combining the fractions, we get:
10/d > 1
To satisfy this inequality, the denominator 'd' must be less than 10. For example, if we choose d = 9, the fractions become 8/9 and 2/9, and their sum is 10/9, which is greater than 1.
In summary, if the sum of the fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.
Learn more about denominator here: https://brainly.com/question/15007690
#SPJ11
If Sample #1 contains 2. 98 moles of hydrogen at 35. 1 degrees C and 2. 3 atm
in a 32. 8 L container. How many moles of hydrogen are in a 45. 3 liter
container under the same conditions?
To calculate the number of moles of hydrogen in a 45.3-liter container under the same conditions as Sample #1, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
Given that Sample #1 contains 2.98 moles of hydrogen at 35.1 degrees C (308.25 K) and 2.3 atm in a 32.8 L container, we can use these values to find the value of R.
R = (PV) / (nT) = (2.3 atm * 32.8 L) / (2.98 moles * 308.25 K)
Once we have the value of R, we can use it to calculate the number of moles in the 45.3-liter container at the same conditions:
n = (PV) / (RT) = (2.3 atm * 45.3 L) / (R * 308.25 K)
By substituting the appropriate values and solving the equation, we can determine the number of moles of hydrogen in the 45.3-liter container.
To learn more about hydrogen: -brainly.com/question/30623765
#SPJ11
Darren lives in Wrexham and works in Corwen.
a) Use the chart to find the road distance
between Wrexham and Corwen.
(a) The road distance between Wrexham and Oswestry is 15 miles.
(b) The number of miles Sarah travels to and from work each week is 330 miles.
Given a chart of the road distances between various towns and cities.
(a) From the chart,
Distance the corresponds to Wrexham and Oswestry = 15 miles
Road distance between Wrexham and Oswestry is 15 miles.
(b) Distance between Ruthin and Oswestry = 33 miles
Total distance travelled to and from work in a day = 33 × 2 = 66 miles
She works 5 days a week.
Total distance travelled for 5 days = 66 × 5 = 330 miles
Hence, the number of miles travelled by Sarah in a week is 330 miles.
Learn more about Arithmetic Operations here :
brainly.com/question/30553381
#SPJ4
The chart is given below.
"Your question is incomplete, probably the complete question/missing part is:"
The chart shows the distances, in miles, between some towns and cities.
Toby lives in Wrexham and works in Oswestry.
Wrexham
18
Ruthin
a) Use the chart to find the road distance
between Wrexham and Oswestry.
15
21
12
Corwen
15
33
23
Oswestry
Sarah lives in Ruthin and works in Oswestry for
5 days a week. Each day she travels to and
from work using the route shown on the map.
MOLD
ROTHEN
WRESTHAM
b) How many miles, in total, does she travel to
and from work each week? 231 miles
CORNEN
OSWESTRY
Choose CI
Annika is planning an event for which the total cost must be no more than $400. Annika plans to spend $180 on decorations and she wants to hire a DJ at the rate of $35 per hour. Which inequality correctly shows Annika’s spending in terms of h, the number of hours that the DJ can be at the party?
the correct inequality that shows Annika's spending in terms of h is 35h + 180 ≤ 400.To express Annika's spending in terms of h, the number of hours the DJ can be at the party, we can set up an inequality by considering the total cost.
Let's represent Annika's spending on the DJ as 35h, where h is the number of hours. Additionally, we know Annika plans to spend $180 on decorations. Therefore, the total cost should be no more than $400.
The inequality can be written as:
35h + 180 ≤ 400
This inequality states that the cost of hiring the DJ (35h) plus the cost of decorations ($180) should be less than or equal to $400.
Therefore, the correct inequality that shows Annika's spending in terms of h is 35h + 180 ≤ 400.
To learn more about cost click here:brainly.com/question/14566816
#SPJ11
Write the equation for the perpendicular bisector of a segment that has endpoints (–1, 10) and (3, 6).
Question 3 options:
A) y = x + 7
B) y = x – 7
C) y = –x + 9
D) y = x + 11
The incenter is the center of the __________ circle.
Question 5 options:
A) inscribed
B) congruent
C) circumscribed
D) acute
Which statement correctly describes the location of the incenter of a triangle?
Question 6 options:
A) The incenter is closest to the shortest side of the triangle.
B) The incenter is closest to the longest side of the triangle.
C) The incenter is equidistant from all three sides of the triangle.
D) The incenter is equidistant from all three vertices of the triangle.
The statement that correctly describes the location of the incenter of a triangle is that the incenter is equidistant from all three sides of the triangle. Therefore, the correct answer is C. The incenter is equidistant from all three sides of the triangle.
The equation for the perpendicular bisector of a segment that has endpoints (–1, 10) and (3, 6) is y
= x + 2.
The steps to solve for the equation of the perpendicular bisector are as follows:Find the midpoint of the segment by averaging the x-coordinates and the y-coordinates of the endpoints:Midpoint
= ( (-1 + 3) / 2, (10 + 6) / 2 )
= (1, 8)
Find the slope of the segment: Slope
= (6 - 10) / (3 - (-1))
= -1Use the negative reciprocal of the slope of the segment to find the slope of the perpendicular bisector:
Slope of perpendicular bisector
= 1 Use the slope and the midpoint to write the equation of the perpendicular bisector in slope-intercept form: y
= mx + b, where m is the slope and b is the y-intercept.8
= 1(1) + b, so b
= 7The equation of the perpendicular bisector is y
= x + 7.
Therefore, the correct answer is A. y
= x + 7.
The incenter is the center of the inscribed circle. Therefore, the correct answer is A. inscribed.The statement that correctly describes the location of the incenter of a triangle is that the incenter is equidistant from all three sides of the triangle. Therefore, the correct answer is C. The incenter is equidistant from all three sides of the triangle.
To know more about equidistant visit:
https://brainly.com/question/29886221
#SPJ11
Meg dilated triangle W by a factor less than 1. Then she performed other transformations that were not dilations to create similar triangle W′. Which could be the vertices of triangle W? A. X(–2, 2), Y(–10, 2), Z(–6, 10) B. X(2, 2), Y(4, 2), Z(3, 4) C. X(0, 2), Y(4, 2), Z(2, –6) D. X(2, 2), Y(2, 6), Z(4, 6).
The answer is C. Triangle W with vertices X(0, 2), Y(4, 2), Z(2, -6) could be dilated by a factor less than 1 and then transformed to create a similar triangle W′.
In a dilation, the sides of the original triangle are stretched or compressed by the same factor to create the sides of the new triangle. Since the factor of dilation in this case is less than 1, the sides of triangle W′ will be shorter than the corresponding sides of triangle W.
Looking at the given options, only triangle W with vertices X(0, 2), Y(4, 2), Z(2, -6) satisfies this condition. The other options either do not have vertices that can be dilated by a factor less than 1 or do not create similar triangles with the desired transformations.
Therefore, option C is the correct choice.
To know more about triangle click here: brainly.com/question/2773823
#SPJ11
Which of the four materials meet the minimum specific heat capacity criteria of at
least 1. 8 J/g °C?
Materials B and D are the only materials mentioned that meet the minimum specific heat capacity requirement of at least 1.8 J/g °C.
Based on the given information, the materials that meet the minimum specific heat capacity criteria of at least 1.8 J/g °C are Materials B and D.
Specific heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount. The minimum requirement is 1.8 J/g °C.
Material B and Material D have specific heat capacities that meet this criteria. The specific heat capacity values for these materials are not provided, but they are known to be at least 1.8 J/g °C.
The specific heat capacities of Materials A and C are not specified, so it cannot be determined whether they meet the minimum criteria.
Therefore, Materials B and D are the only materials mentioned that meet the minimum specific heat capacity requirement of at least 1.8 J/g °C.
Learn more about specific heat here : brainly.com/question/31608647
#SPJ11
Which polynomial is the correct product? 15y3 17y2 22y 15 6y3 17y2 22y 15 6y3 20y2 22y 15 6y3 17y2 22y 25.
The correct polynomial product is indeed Option B: 6y^3 + 17y^2 + 22y + 15.
Let's break down the options to see why Option B is correct:
Option A: 15y^3 + 17y^2 + 22y + 15
This option does not match the given product as it includes an additional term, 15y^3, that is not present in the correct polynomial product.
Option B: 6y^3 + 17y^2 + 22y + 15
This option matches the given polynomial product exactly. It includes all the terms and coefficients mentioned: 6y^3, 17y^2, 22y, and 15.
Option C: 6y^3 + 20y^2 + 22y + 15
This option differs from the correct product in the coefficient of the second term. It includes 20y^2 instead of 17y^2.
Option D: 6y^3 + 17y^2 + 22y + 25
This option differs from the correct product in the coefficient of the last term. It includes 25 instead of 15.
Therefore, Option B, 6y^3 + 17y^2 + 22y + 15, is the correct polynomial product based on the given information.
for such more question on polynomial
https://brainly.com/question/7297047
#SPJ8
What is the quotient of (x3 – 3x2 5x – 3) ÷ (x – 1)?.
The quotient of (x³ – 3x² + 5x – 3) ÷ (x – 1) can be found by using long division. First, we place the dividend, which is x³ – 3x² + 5x – 3, inside the division symbol. Then, we divide the first term of the dividend, which is x³, by the divisor, which is x – 1. This gives us x² as our first term of the quotient.
We then multiply x² by the divisor, which gives us x³ – x². We subtract this from the dividend to get -2x² + 5x – 3.We then bring down the next term of the dividend, which is 0x² + 5x. We repeat the process of dividing, multiplying, subtracting, and bringing down until we reach the end of the dividend. This gives us the quotient as x² + 2x + 5 and a remainder of 2x – 3.We have a polynomial division, x³ – 3x² + 5x – 3 ÷ x – 1. Using polynomial division, we can find the quotient and remainder when dividing one polynomial by another. Let's go through the process of polynomial division step-by-step:
We will first divide the x³ by x, which gives us x². We will then multiply x² by the divisor x – 1, which gives us x³ – x². We will subtract this from the original polynomial, x³ – 3x² + 5x – 3 – (x³ – x²) = -2x² + 5x – 3.Next, we will divide -2x² by x, which gives us -2x. We will then multiply -2x by the divisor x – 1, which gives us -2x² + 2x. We will subtract this from the polynomial we obtained in the previous step, -2x² + 5x – 3 – (-2x² + 2x) = 3x – 3.Finally, we will divide 3x by x, which gives us 3. We will then multiply 3 by the divisor x – 1, which gives us 3x – 3. We will subtract this from the polynomial we obtained in the previous step, 3x – 3 – (3x – 3) = 0.Remember that the quotient of a polynomial division is the polynomial that we obtain after performing all the steps of polynomial division. Therefore, the quotient in this case is x² – 2x + 3. The remainder is 0, which means that the polynomial x³ – 3x² + 5x – 3 is evenly divisible by x – 1.
To conclude, the quotient of (x³ – 3x² + 5x – 3) ÷ (x – 1) is x² – 2x + 3. The remainder is 0, which means that the polynomial x³ – 3x² + 5x – 3 is evenly divisible by x – 1.
To know more about polynomial division:
brainly.com/question/29193026
#SPJ11
If a bookseller earns a profit of 25 percentage by selling a novel worth rs 300 calculate the selling price of the novel
The selling price of the novel would be Rs 375. The bookseller should sell the novel for Rs 375 to earn a profit of 25%. Profit percentage is a measure of the profit earned as a percentage of the cost price.
In this case, the bookseller earns a profit of 25%. To calculate the selling price, we need to determine the profit earned and add it to the cost price.
To find the profit earned, we multiply the cost price by the profit percentage. In this case, the cost price of the novel is given as Rs 300, and the profit percentage is 25%. To calculate the profit, we multiply Rs 300 by (25/100) or 0.25. The result is Rs 75, indicating that the bookseller earns a profit of Rs 75.
To obtain the selling price, we add the profit to the cost price. In this case, the cost price is Rs 300, and the profit is Rs 75. Adding them together, we get Rs 375 as the selling price of the novel.
To calculate the selling price, we need to determine the profit earned by the bookseller and add it to the cost price.
Given:
Profit percentage = 25%
Cost price of the novel = Rs 300
To calculate the profit, we multiply the cost price by the profit percentage:
Profit = 25% of Rs 300 = (25/100) * 300 = Rs 75
The selling price is obtained by adding the profit to the cost price:
Selling price = Cost price + Profit = Rs 300 + Rs 75 = Rs 375.
Therefore, the selling price of the novel is Rs 375.
Learn more about profit here: brainly.com/question/32381738
#SPJ11
For the functions f(x)=3x2+3x+2andg(x)=2x2−2x+3, find:
The sum of f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3 is 5x^2 + x + 5, while the difference is x^2 + 5x - 1. These results are obtained by adding and subtracting the corresponding terms of the two functions.
To find the sum and difference of the functions f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3, we add and subtract the corresponding terms.
For the sum, we add the like terms: (3x^2 + 2x^2) + (3x - 2x) + (2 + 3) = 5x^2 + x + 5.
For the difference, we subtract the like terms: (3x^2 - 2x^2) + (3x + 2x) + (2 - 3) = x^2 + 5x - 1.
Therefore, the sum of the functions is given by f(x) + g(x) = 5x^2 + x + 5, and the difference of the functions is given by f(x) - g(x) = x^2 + 5x - 1.
To learn more about sum and difference click here
brainly.com/question/29774937
#SPJ11
Kent put $8,500 into an 18 month CD. The interest rate is 3.25% How much money will Kent earn in interest?
Kent will earn $553.12 in interest from his 18-month CD with an interest rate of 3.25%.
To calculate the interest earned, we can use the formula: Interest = Principal × Rate × Time. In this case, the principal (amount invested) is $8,500, the interest rate is 3.25% (or 0.0325 as a decimal), and the time is 18 months (or 1.5 years). Plugging in these values into the formula, we get: Interest = $8,500 × 0.0325 × 1.5 = $553.12. Therefore, Kent will earn $553.12 in interest from his CD.
It's important to note that the interest rate is typically expressed as an annual rate. In this case, the interest rate is 3.25%, which means that for a full year, Kent would earn 3.25% of the principal amount. However, since the CD term is 18 months (or 1.5 years), we need to adjust the formula accordingly. By multiplying the principal by the interest rate and the time, we can determine the total interest earned over the given period. In this case, the interest earned is $553.12.
Learn more about interest here:
https://brainly.com/question/8100492
#SPJ11
It is 185 miles to Fort Worth if vangs drives 2 hours at 65 miles per hour how far will he be from Fort Worth
If Vangs drives for 2 hours at a speed of 65 miles per hour, we can calculate how far he will be from Fort Worth. Vangs will be 125 miles away from Fort Worth.
Given that Vangs drives at a speed of 65 miles per hour for 2 hours, we can calculate the distance traveled using the formula Distance = Speed × Time.
Distance = 65 miles/hour × 2 hours = 130 miles.
Since Vangs started 185 miles away from Fort Worth and traveled a distance of 130 miles, we subtract the distance traveled from the initial distance to find how far he will be from Fort Worth.
Distance from Fort Worth = Initial distance - Distance traveled = 185 miles - 130 miles = 55 miles.
Therefore, Vangs will be 55 miles away from Fort Worth after driving for 2 hours at a speed of 65 miles per hour.
To learn more about Speed - brainly.com/question/32673092
#SPJ11
If G is the incenter of AABC, find each measure.
Therefore, the measures of the angles AGB, BGC, and AGC are given by:$$m\angle AGB=\frac{180^\circ}{\pi}\cdot \arctan\frac{z}{x+y+z}$$$$m\angle BGC=\frac{180^\circ}{\pi}\cdot \arctan\frac{y}{z}$$$$m\angle AGC=\frac{180^\circ}{\pi}\cdot \arctan\frac{x}{z}$$Thus, the solution is obtained.
Given that G is the incenter of the triangle AABC.The incenter of a triangle is the intersection point of the angle bisectors of the triangle's three angles.We have to find the measure of the angles AGB, BGC, and AGC.
Solution:Let us consider the figure below: [asy]
pair A,B,C,I; A=(-6,-3); B=(4,-3); C=(0,6); draw(A--B--C--A); I=incenter(A,B,C); draw(incircle(A,B,C)); draw(A--I--B); draw(I--C); dot(A); dot(B); dot(C); dot(I); label("$A$",A,WSW); label("$B$",B,ERS); label("$C$",C,N); label("$G$",I,NW); label("$a$",(B+C)/2,E); label("$b$",(A+C)/2,NW); label("$c$",(A+B)/2,SW); label("$x$",(I+B)/2,W); label("$y$",(I+C)/2,NE); label("$z$",(A+I)/2,NW); [/asy]
We can use the angle bisector theorem to determine the measure of the angles AGB, BGC, and AGC.Let $AB=c$, $AC=b$, and $BC=a$. Let $x$, $y$, and $z$ be the lengths of the line segments as shown in the figure above.
By the angle bisector theorem, we know that:$$\frac{AG}{BG}=\frac{b}{a}$$$$\frac{BG}{CG}=\frac{c}{b}$$$$\frac{CG}{AG}=\frac{a}{c}$$
Multiplying these three equations, we get:$$\frac{AG}{BG}\cdot \frac{BG}{CG}\cdot \frac{CG}{AG}=\frac{b}{a}\cdot \frac{c}{b}\cdot \frac{a}{c}=1$$
Thus, we have:$$\frac{x}{z}\cdot \frac{z}{y}\cdot \frac{y}{x}=1$$$$\Rightarrow \frac{x}{y}=\frac{z}{x+y+z}$$
Therefore:$$m\angle AGB=\frac{180^\circ}{\pi}\cdot \arctan\frac{x}{y}=\frac{180^\circ}{\pi}\cdot \arctan\frac{z}{x+y+z}$$
Similarly, we can show that:$$m\angle BGC=\frac{180^\circ}{\pi}\cdot \arctan\frac{y}{z}$$$$m\angle AGC=\frac{180^\circ}{\pi}\cdot \arctan\frac{x}{z}$$.
To know more about incenter :
https://brainly.com/question/22369775
#SPJ11
A group of 5 friend were bowling one Saturday night. There are 10 pins in bowling and 10 frames for each bowler. If every bowler knocked every pin down every frame, how many pins would be knocked down?
250 pins would be knocked down.
In bowling, a single bowler would knock down all ten pins in every frame; thus, a total of 10 frames will result in 100 knocked down pins for each bowler. So, five bowlers each knocking down 100 pins would result in a total of 500 pins knocked down. Consequently, all 50 pins would be knocked down in total (100 pins per bowler × 5 bowlers), which amounts to 250 knocked down pins.
Therefore, the main answer is 250 pins would be knocked down.
To know more about bowling, click here
https://brainly.com/question/30928102
#SPJ11
Select the correct answer.
Solve the exponential equation for X.
216 6(41 +11)
OA.
I = 2
OB.
I = -2
OC.
I = 3
OD.
= -3
The given equation is I = -2OD where I is the intensity of light, O is the aperture of the lens and D is the distance between the lens and the object. This equation is known as the Inverse Square Law of Light.
The equation states that the intensity of light decreases as the square of the distance between the object and the ens increases. This means that if we double the distance between the object and the lens, the intensity of light becomes 1/4th of its original value.Similarly, if we triple the distance between the object and the lens, the intensity of light becomes 1/9th of its original value. This law is applicable to all types of light sources, including natural light sources like the sun and artificial light sources like bulbs.One practical application of this law is in photography. If a photographer wants to capture an image of a subject that is far away, they need to use a lens with a larger aperture to let in more light. This will ensure that the image is bright and clear even when the distance between the subject and the camera is large.Similarly, if a photographer wants to capture an image of a subject that is close to the camera, they need to use a lens with a smaller aperture to reduce the amount of light that enters the camera. This will prevent the image from being overexposed and washed out.Overall, the Inverse Square Law of Light is an important principle that governs the behavior of light in various applications, including photography, cinematography, and physics.For such more question on Square Law
https://brainly.com/question/30404562
#SPJ8
Suppose that the function f(x) = 5.32 + 0.80x represents the cost of mailing an object that weighs x pounds. What is f(36)?
The value of function at x = 36 is 34.12.
To find the cost of mailing an object that weighs 36 pounds, we can substitute the value of x into the function f(x) = 5.32 + 0.80x.
The function f(x) = 5.32 + 0.80x represents a linear relationship between the weight of the object (x) and the cost (f(x)) with a base cost of $5.32 and an additional cost of $0.80 per pound. By plugging in the value of 36 into the function, we can calculate the specific cost for that weight.
Plugging in x = 36, we have:
f(36) = 5.32 + 0.80 * 36
Simplifying the expression:
f(36) = 5.32 + 28.8
f(36) = 34.12
Therefore, f(36) is equal to 34.12. This means that it would cost $34.12 to mail an object weighing 36 pounds according to the given function.
Learn more about Function here
https://brainly.com/question/18302067
#SPJ4
A photon has a frequency of 2. 9 × 10–16 Hz. Planck’s constant is 6. 63 × 10–34 J•s. The energy of the photon, to the nearest tenths place, is × 10–49 J.
Using the equation E = hf, where f = 2.9 × 10^(-16) Hz and h = 6.63 × 10^(-34) J·s, the energy of the photon is approximately 1.9 × 10^(-49) J.
To calculate the energy of a photon, you can use the equation:
E = hf
where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon.
Given:
Frequency (f) = 2.9 × 10^(-16) Hz
Planck's constant (h) = 6.63 × 10^(-34) J·s
Now, substitute the values into the equation:
E = (6.63 × 10^(-34) J·s) × (2.9 × 10^(-16) Hz)
Multiply the values:
E = 1.9207 × 10^(-49) J
To the nearest tenths place, the energy of the photon is approximately 1.9 × 10^(-49) J.
To learn more about photon click here brainly.com/question/28134171
#SPJ11
Tommy walks 2 miles to school each morning. During his walk he sees billboards every 1/5 of a mile. How many billboards does he see each morning?
Tommy walks 2 miles to school each morning, and he sees a billboard every 1/5 of a mile.
To find out how many billboards he sees, we can divide the total distance he walks (2 miles) by the distance between each billboard (1/5 of a mile).
Number of billboards = Total distance / Distance between billboards
= 2 miles / (1/5 mile)
= 2 miles * (5/1)
= 10 billboards
Therefore, Tommy sees 10 billboards each morning.
learn more about:- billboards here
https://brainly.com/question/31623835
#SPJ11
A man sets out to travel from A to C via B. From A he travels 8km on a bearing N30°E to B. From B, he travels a further 6km due East. Calculate how far C is (i) North of A (ii) east of A?
He travels: (i) C is 4 km north of A. (ii) C is 6 km east of A.
How to Calculate how far C is (i) North of A (ii) east of A(i) North of A:
The northward component from A to B is 8 km on a bearing of N30°E. To find the northward distance, we can use trigonometry. Since the bearing is N30°E, we can split it into two right-angled triangles: one facing north and one facing east.
In the northward triangle:
Opposite side = 8 km * sin(30°)
Opposite side = 8 km * 0.5
Opposite side = 4 km
Therefore, C is 4 km north of A.
(ii) East of A:
The eastward component from B to C is 6 km due East. Since this distance is directly east, it does not change the eastward position of C relative to A. Therefore, C is 6 km east of A.
Learn more about bearing at https://brainly.com/question/28782815
#SPJ4
Jema has a 45% coupon for a new curling iron. She buys the curling iron for a final price of $49. 95 after the discount is taken off. What is the original cost of the curling iron? Round to the nearest cent if necessary
The original cost of the curling iron was approximately $90.82.
Jema had a 45% coupon for a new curling iron, which means she was eligible for a discount of 45% on the original cost of the curling iron. The final price she paid after the discount was $49.95. To find out the original cost of the curling iron, we can use the formula:
Original cost = Final price / (1 - Discount rate)
In this case, since the discount rate is 45%, or 0.45 as a decimal, the formula becomes:
Original cost = $49.95 / (1 - 0.45)
Original cost = $49.95 / 0.55
Original cost ≈ $90.82
Therefore, the original cost of the curling iron was approximately $90.82.
This calculation shows that Jema took advantage of a significant discount on the original cost of the curling iron. By using the coupon, she was able to save around $41.87 on the purchase. This demonstrates the importance of looking for discounts and deals when shopping, as they can help save money and get more value for your purchases.
learn more about original cost here
https://brainly.com/question/7568734
#SPJ11
The dimensions of a right recutangular prism are 0.25m, 0.36m, and 0.14mWhat is the volume of the prism? use the formula v=1xwxh
The volume of the given right rectangular prism is 0.0126 m³.
The volume of a right rectangular prism can be calculated using the formula:
V = l × w × h,
where l, w, and h are the dimensions of the prism.
The given dimensions of the right rectangular prism are 0.25m, 0.36m, and 0.14m.
Volume of the prism = l × w × h
= 0.25 × 0.36 × 0.14
= 0.0126 m³
Therefore, the volume of the prism is 0.0126 m³.
We have used the formula:
V = l × w × h to find out the volume of the prism.
This is because the given prism is a right rectangular prism.
The formula for finding the volume of a right rectangular prism is
V = l × w × h,
where l, w, and h are the dimensions of the prism.
A right rectangular prism is a three-dimensional figure with six rectangular faces.
It has three pairs of congruent faces that are parallel to each other.
The opposite faces of the right rectangular prism are identical in size and shape.
The right rectangular prism is a type of prism, which is a three-dimensional figure with two identical and parallel faces called bases.
A prism can be named by the shape of its base. In this case, the right rectangular prism has a rectangular base.
Conclusion: The volume of the given right rectangular prism is 0.0126 m³, which was found using the formula V = l × w × h.
To know more about rectangular prism, visit:
https://brainly.com/question/29753475
#SPJ11
Alli has $382. 45 in her checking account and $450 in her savings account. She writes a check for $400. Alli’s bank automatically takes money from her savings to cover the amount of a check if the money in the checking account is not sufficient. Unfortunately for Alli, the bank also withdraws $25 from her savings account for this service. Once the check has cleared, how much money does Alli have in her savings account?
$17. 55
$17. 55
$42. 55
$42. 55
$407. 45
$407. 45
$442. 55
$442. 55
Once the check has cleared, Alli has $17.55 in her savings account. Finally, the amount of money Alli has in her savings account after the check has cleared is $25, so the answer is option A: $17.55.
Initial amount in Alli's checking account = $382.45
Initial amount in Alli's savings account = $450
Amount Alli withdrew from checking account = $400
Amount the bank withdrew from Alli's savings account = $25
Total cost of the check = 400+25
=425
Since the initial amount in her checking account was insufficient, the bank automatically withdrew $25 from her savings account to cover the cost of the check. This means that Alli has a total of $425 - $400 = $25 left in her savings account.After the withdrawal from her savings account, Alli's remaining savings balance is $450 - $25 = $425. However, she spent $400 to cover the check, so her final savings balance is $425 - $400 = $25.
To know more about savings account visit :-
https://brainly.com/question/1446753
#SPJ11
The owner of an ice cream shop have determined that their daily revenue and cost in dollars are given by R = 4.15x C = 3.20x + 798 where x is the number of scoops served in a day
The daily revenue (R) is given by R = 4.15x, and the daily cost (C) is given by C = 3.20x + 798, where x is the number of scoops served in a day.
In more detail, the given equations represent a linear relationship between the number of scoops served (x) and both the revenue (R) and cost (C). The coefficient of x in the revenue equation, 4.15, represents the revenue generated per scoop served. Similarly, the coefficient of x in the cost equation, 3.20, represents the cost incurred per scoop served. The constant term 798 in the cost equation represents additional fixed costs.
To determine the daily profit, we can subtract the cost from the revenue: Profit = R - C = 4.15x - (3.20x + 798) = 0.95x - 798. This equation allows us to calculate the profit based on the number of scoops served.
Learn more about generated per scoop served here:
https://brainly.com/question/28706292
#SPJ11
B.
zoom in
Find the value of the variables for
which ABCD must be a parallelogram.
~ 3x
X
3
3y
3y
D
21
Required
X =
?/1
I
22
Required
y =
?/1
.
D
The value of the variables for which ABCD must be a parallelogram include the following:
x = 4.
y = 5.
How to determine value of the variables for ABCD?In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:
Line segment AC = Line segment BD
Next, we would write an equation to model the length of the diagonals of this parallelogram as follows;
4x - 2 = 3y - 1 .........equation 1.
3y - 3 = 3x .........equation 2.
From equation 2, we have the following:
y - 1 = x .........equation 3.
By substituting equation 3 into equation 1, we have:
4(y - 1) - 2 = 3y - 1
4y - 4 - 2 = 3y - 1
4y - 3y = 6 - 1
y = 5.
For the value of x, we have:
x = y - 1
x = 5 - 1
x = 4
Read more on a parallelogram here: brainly.com/question/31416609
#SPJ4
Complete Question:
Find values of x and y for which ABCD must be a parallelogram.
a cone with equal height and radius has volume 1234 cm³. what is the height of the cone to the nearest tenth of a centimetre?
The height is equal to the radius, the height of the cone to the nearest tenth of a centimetre is 14.98 cm. A cone with equal height and radius has volume 1234 cm³. To find the height of the cone, we will use the formula for the volume of a cone: V = 1/3πr²h
A cone with equal height and radius has volume 1234 cm³. To find the height of the cone, we will use the formula for the volume of a cone: V = 1/3πr²h
where: V is the volume of the cone, π is pi (3.14), r is the radius of the cone, h is the height of the cone
We are given that the height and radius of the cone are equal, so we can substitute r for h. Also, we know the volume of the cone is 1234 cm³. So:
1234 = 1/3πr²h
1234 = 1/3πr²(r)
1234 = 1/3πr³ (since r = h)
Now we can solve for r: 1234 * 3 / π = r³
3747.22 = r³
r ≈ 14.98 cm
Since the height is equal to the radius, the height of the cone to the nearest tenth of a centimetre is 14.98 cm.
To know more about cone visit: https://brainly.com/question/10670510
#SPJ11
Sandra calculated her taxable income as 39,250. She paid 6,000 in federal withholding tax. What is the amount of Sandra will receive as a refund
Sandra will receive a refund of $1,290 from the Internal Revenue Service. She wants to know how much she will receive as a refund from the Internal Revenue Service (IRS).
It is an agency under the U.S. Department of the Treasury. The amount of Sandra will receive as a refund is calculated as follows: Her total federal tax owed is calculated as a percentage of her taxable income. For the 2019 tax year, the percentage tax rates for single filers are as follows:10% on taxable income from $0 to $9,700,12% on taxable income over $9,700 to $39,475, and 22% on taxable income over $39,475 to $84,200. Sandra's taxable income is within the 12% tax bracket.
She owes 12% of her taxable income in federal taxes. This can be calculated as follows:
12% x $39,250 = $4,710
Her total federal tax owed is $4,710. However, she already paid $6,000 in federal withholding tax. Therefore, her refund can be calculated as follows:
Refund = Amount withheld - Amount owed Refund
= $6,000 - $4,710
Refund = $1,290
To know more about Internal Revenue Service visit:
https://brainly.com/question/30401300
#SPJ11
[tex]y=-3x^{2} -6x+8[/tex] the x-interval over which the function is increasing
The x-interval over which the function is increasing is:x < -1 or x > -1
Given function:[tex]y=-3x^{2} -6x+8[/tex]
The x-interval over which the function is increasing.
The given function is a quadratic function of the form f(x) = ax² + bx + c. We will determine the intervals for which the function is increasing.
To know the increasing intervals of the given function f(x), we need to determine the intervals for which f'(x) > 0 where f'(x) is the first derivative of the function.
So, Let's find the first derivative of the given function:
[tex]\begin{aligned}f(x)&=-3x^{2}-6x+8\\\Rightarrow f'(x)&=-6x-6=-6(x+1)\end{aligned}[/tex]
Now, we have to check the sign of f'(x) to find the interval(s) where the function is increasing.
Sign of f'(x) changes at x = -1. If x < -1, f'(x) > 0, so the function is increasing in that interval. Similarly, if x > -1, f'(x) > 0, so the function is increasing in that interval as well.
Therefore, the x-interval over which the function is increasing is:x < -1 or x > -1
To know more about functions visit:
https://brainly.com/question/11624077
#SPJ11
The(mean, Mean absolute deviation) is greater for this year's 100-meter dash, which suggests that all 30 students(improved, did not improve) equally.
The statement "all 30 students improved equally" is not supported by the fact that the MAD is greater.
We have,
The mean absolute deviation (MAD) measures the average distance between each data point and the mean of a dataset.
If the MAD is greater for this year's 100-meter dash compared to the previous year, it indicates a higher variability or spread in the performance of the 30 students.
If all 30 students improved equally, it would result in a more consistent performance across the group, leading to a lower MAD.
Therefore,
The statement "all 30 students improved equally" is not supported by the fact that the MAD is greater.
Learn more about MAD here:
https://brainly.com/question/32035745
#SPJ4
A right triangle has legs measuring 18 in. And 26 in. What is the length of the hypotenuse? Round to the nearest tenth. 18. 8 in. 31. 6 in. 44. 0 in. 100. 0 in.
Right triangle, the hypotenuse is the longest side and is opposite the right angle. The length of the hypotenuse of the right triangle is approximately 31.6 in.
In a right triangle, the hypotenuse is the longest side and is opposite the right angle. To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two legs.
Let's denote the length of the legs as a = 18 in and b = 26 in. The Pythagorean theorem can be written as:
c^2 = a^2 + b^2
Substituting the values, we have:
c^2 = 18^2 + 26^2
= 324 + 676
= 1000
Taking the square root of both sides, we find:
c = √1000
≈ 31.6
Therefore, the length of the hypotenuse is approximately 31.6 in, rounded to the nearest tenth.
Learn more about hypotenuse here:
https://brainly.com/question/16893462
#SPJ11
