Sammy's dog eats 3/4 cup of food at each meal. His cat eats 1/8 of what the dog eats. What fraction of a cup does his cat eat?
Answer:
3/32 of a cup of food
Step-by-step explanation:
Sammy's dog eats 3/4 cup of food at each meal. His cat eats 1/8 of that.
This comes out to (1/8)th of (3/4 cup), or:
1 3
----- · ----- cup = 3/32 cup
8 4
The cat eats 3/32 of a cup of food.
Final answer:
Sammy's cat eats 3/32 cup of food per meal, which is calculated by multiplying the dog's portion, 3/4 cup, by 1/8.
Explanation:
Solving the question involves a basic understanding of fractional multiplication. Since Sammy's cat eats 1/8 of what the dog eats, we calculate the cat's portion by multiplying the dog's portion by 1/8.
Sammy's dog eats 3/4 cup of food at each meal. To find out what fraction of a cup Sammy's cat eats, we multiply 3/4 by 1/8.
Here's the calculation: 3/4 × 1/8 = 3/32
Therefore, Sammy's cat eats 3/32 cup of food at each meal.
Theres 5 boxes of candle. One box has 16 candles Four boxes has 24 candles each How many candles do the five boxes have altogether?
Answer:
112 candles
Step-by-step explanation:
We can simply add up the 5 numbers of candles, or we can take advantage of the invention of multiplication to replace repeated addition. The number of candles altogether is the sum of the numbers of candles in each of the 5 boxes.
16 + 4×24 = 16 +96 = 112
The total number of candles is 112.
A baseball infield is in the shape of a square within the bases and home plate. The area of the infield is 8,100 square feet. What is the length of one side of the infield?
HELP WILL PICK BRAINLIEST!
Choose the correct domain for f(x) = ex -2
(-∞,∞)
(0,∞)
[0,∞)
(-∞,0)
Answer:
The function has no undefined points nor domain constraints, therefore the Domain is (-∞ < x < ∞). Since your answers don't match the real results, the interval notation is (-∞,∞)
Step-by-step explanation:
What is the distance between the 2 points? ( use Pythagorean Theorem)
Answer:
5
Step-by-step explanation:
The horizontal distance between the points is 3 units; the vertical distance is 4 units. The straight-line distance is the length of the hypotenuse of a right triangle with those side lengths. So, the distance between the two points is ...
√(3² +4²) = √(9+16) = √25 = 5 . . . . units
_____
Comment on this triangle
The numbers 3, 4, 5 are the smallest set of integers that satisfy the relation of the Pythagorean theorem. They are also the only set of sequential numbers or numbers in arithmetic sequence that satisfy the Pythagorean theorem. As a consequence, they show up often in geometry and algebra problems. The "3-4-5 triangle" is worth remembering. So, anytime you see numbers that have these ratios, such as 9, 12, 15, for example, you know they can be the sides of a right triangle.
What is the value of 6x squared+ 4x + 8 when x=7? Please answer this I really need help!
Mateo wants to make a toy sailboat. He has two pieces of wood to choose from.
His first piece of wood is a block that measures 18'' x 10" x 8". It weighs 46.65 lbs.
His second piece of wood is a log of wood measuring 21" long, with an average circumference of 25.12". It weights 39.25 lbs.
The sailboat needs to float, but both blocks of wood are denser than wood usually is, and he's not sure either piece of wood will float. He doesn't want to get the water wet before he's applied a sealant, so he isn't willing to just drop them in the water to find out.
2a. Which common solid can he use to represent the block? Which common solid can he use to represent the log? (2 points)
2b. What is the density of the block in pounds per cubic inch? Give the formula for density and show your work. (3 points)
2c. What is the density of the log in pounds per cubic inch? Give the formula for density and show your work. Use 3.14 for π. (Hint: you can determine the radius from the circumference.) (3 points)
2d. Water has a density of about 0.0361 pounds/cubic inch. Anything rarer will float, and anything denser will sink. Which of the pieces of wood are suitable for making a toy boat that will float? (2 points)
Answer:
wut is it
Step-by-step explanation:
What is the standard form of the equation for this circle?
A. -(x – 1)2 – (y + 10)2 + 4 = 0
B. (x – 1)2 – (y + 10)2 = 2
C. (x + 1)2 + (y – 10)2 = 4
D. (x – 1)2 – (y + 10)2 = 4
A (-1, 10)
Radius 2
Answer:
C
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h. k) are the coordinates of the centre and r is the radius
here (h, k) = (- 1, 10) and r = 2, thus
(x - (- 1))² + (y - 10)² = 2², that is
(x + 1)² + (y - 10)² = 4 → C
Please help me with this problem.
Answer:
Step-by-step explanation:
It would help you if you drew charts of what is happening. The red tank is loosing volume. It's chart is on the left.
The blue tank is gaining water (the same amount as the red is loosing)
The red graph is the red tank.
The blue graph is the blue tank.
All you really have to understand is the the slopes (3 and - 3) and the same numerically and the rates are the same numerically. So the negative slope means loose. and the positive slope (blue) gains.
The graphs have to start somewhere. You can't make a graph like one without a starting point.
The blue container starts at 0,0. I think that's easy enough to understand. At the beginning of your experiment, the blue container is empty.
The red container starts (arbitrarily) at 3 (the y intercept). It is just a number. It means that the red container starts with 3 gallons.
Neither graph should go into a negative region. I don't know how to make desmos not go into a negative region. Just block them out in your mind. Everything should take place in quadrant 1 bound by the +x and + y axis.
The red object below, is best defined as a
Answer:
Where is the red object?
Step-by-step explanation:
I CANT SEE THE RED OBJECT U DIDNT PUT ITTT
Tell whether this set of numbers is a Pythagorean Triple. (15, 20, 25). Yes or no?
The dimensions of Square A are three times The dimensions of Square B. The area of Square A is 1,296 cm2. What is the area of Square b?
Square B Area = 144cm²
Square B = X
The dimensions of Square A are three times The dimensions of Square B
Square A = 3 * Square B
Square A = 3X
The area of Square A is 1,296 cm2.
Square A Area = (3X)² = 1296
Square B Area = X²
Solve to find X.
(3X)² = 1296
3X = 36
X = 36/3 = 12
Square B Area = 12² = 144
Square B Area = 144cm²
Final answer:
The area of Square B is 144 cm², calculated by dividing the area of Square A (1,296 cm²) by 9, because the area of a square scales with the square of its linear dimensions.
Explanation:
The area of Square A is given as 1,296 cm². Since the dimensions of Square A are three times the dimensions of Square B, we can find the area of Square B by understanding that area scales in proportion to the square of the linear dimensions. This means that if one dimension is three times another, the area will be nine times (3² = 9) larger.
To find the area of Square B, we simply divide the area of Square A by 9:
Area of Square B = Area of Square A / 9
Area of Square B = 1,296 cm² / 9
Area of Square B = 144 cm².
Therefore, the area of Square B is 144 cm².
NEED HELP ASAP! PLEASE HElp!!
the answer should be C
(a) What is the difference between a sequence and a series? A sequence is an unordered list of numbers whereas a series is the sum of a list of numbers. A series is an unordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is an unordered list of numbers. A series is an ordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers. (b) What is a convergent series? What is a divergent series? A series is convergent if the nth term converges to zero. A series is divergent if it is not convergent. A series is convergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent. A series is divergent if the sequence of partial sums is a convergent sequence. A series is convergent if it is not divergent. A convergent series is a series for which lim n → ∞ an exists. A series is convergent if it is not divergent. A series is divergent if the nth term converges to zero. A series is convergent if it is not divergent.
Answer:
a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers; b) A series is divergent if it is not convergent. A series is convergent if the sequence of partial sums is a convergent sequence.
Step-by-step explanation:
A sequence is a pattern. It is an ordered list of objects, such as numbers, letters, colors, etc.
A series is a sum of a sequence.
A divergent series is one that is not convergent.
A convergent series is one in which the sequence of partial sums approaches a limit; this means the partial sums form a convergent sequence.
If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given byP(x) = p(1-p)^(x-1)where p is the probability of success on any one trial.Assume that the probability of a defective computer component is 0.34. Find the probability that the first defect is found in the second component tested.(Round answer to four decimal places.)P(2) =
Answer:
0.2312
Step-by-step explanation:
Using the formula given,
[tex]P(x) = p(1-p)^{x-1}[/tex],
we use 0.34 for p and 2 for x:
[tex]P(2) = 0.34(1-0.34)^{2-1}\\\\P(2) = 0.34(0.68)^1\\\\P(2) = 0.34(0.68) = 0.2312[/tex]
a scientist is growing bacteria in a lab for study one particular type of bacteria grows at a rate of y=2t^2+3t+500 a different bacteria grows at a rate of y=3t^2+t+300 in both of these eqiations y is the number of bacteria after t minutes when is there an equal number of both types of bacteria
Find the length of the missing side. the triangle not drawn to scale. (Image attached)
Will give BRAINLIEST to the first person to answer correctly and show your work please :))
Answer: 8
Step-by-step explanation:
The triangle shown in the image attached is a right triangle.
Therefore, to calculate the missing lenght of the triangle you can apply the Pythagorean Theorem, which is shown below:
[tex]a^2=b^2+c^2[/tex]
Where a is the hypotenuse and b and c are the legs.
The problem gives you the value of the hypotenuse and the value of one leg. Therefore, you must solve for the other leg from [tex]a^2=b^2+c^2[/tex], as following:
[tex]17^2=15^2+c^2\\c=\sqrt{17^2-15^2}\\c=8[/tex]
Therefore, the lenght of the missing side is: 8
Answer:
The value of third side= 8 units
Step-by-step explanation:
It is given a right angled triangle with base = 15 and hypotenuse = 17
We have to find the height of given triangle.
Points to remember
By Pythagorean theorem
Base² + Height² = Hypotenuse²
To find the third side
Here base = 15 and hypotenuse = 17
We have,
Base² + Height² = Hypotenuse²
Height² = Hypotenuse² - Base² = 17² - 15² = 64
Height = √64 = 8 units
Therefore the value of third side = 8 units
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 5(1 − x)−2 f(x) = ∞ n = 0 Find the associated radius of convergence R. R =
We can use the fact that, for [tex]|x|<1[/tex],
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
Notice that
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}[/tex]
so that
[tex]f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right][/tex]
[tex]f(x)=\displaystyle5\sum_{n=0}^\infty nx^{n-1}[/tex]
[tex]f(x)=\displaystyle5\sum_{n=1}^\infty nx^{n-1}[/tex]
[tex]f(x)=\displaystyle5\sum_{n=0}^\infty(n+1)x^n[/tex]
By the ratio test, this series converges if
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)x^{n+1}}{(n+1)x^n}\right|=|x|\lim_{n\to\infty}\frac{n+2}{n+1}=|x|<1[/tex]
so the series has radius of convergence [tex]R=1[/tex].
The Maclaurin series for the function 5(1 − x)⁻² is obtained by applying the binomial series theorem, resulting in the series: 5*(1 + 2x - 2 + 3x² - 3x + 4x³ - 4x² + ...). The radius of convergence for the series is 1.
Explanation:The function given is f(x) = 5(1 − x)−2. The Maclaurin series of a function f is the expression of that function as an infinite sum of terms calculated from the values of its derivatives at a single point. Here, we can use the binomial theorem as a starting point. It states that (1+x)ⁿ = 1 + nx + (n(n-1)/2!)x² + ..., where n is a real number and -1
Now, f(x) is similar to the binomial series: if we let n=-2, and x become -(x-1), we have f(x) = 5(1 – x)⁻² = 5*(1 + 2(x-1) + 3*(x-1)² + 4*(x-1)³ + ...)
So the Maclaurin series for the function is: 5*(1 + 2x - 2 + 3x² - 3x + 4x³ - 4x² + ...). The next step is to find the radius of convergence. The series has a radius of convergence R such that for all x in the interval -R
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Please help me with this...
3x+4=5x-50
54=2x
27=x
Answer:
x = 27
Step-by-step explanation:
The diagonals of a rectangle are congruent, hence
BD = AC ← substitute values
5x - 50 = 3x + 4 (subtract 3x from both sides )
2x - 50 = 4 ( add 50 to both sides )
2x = 54 ( divide both sides by 2 )
x = 27
LAST QUESTION PLEASE HELP ME
Answer:
y = 3x^2 + 1/3
Step-by-step explanation:
The first step is the easiest. Find the value of c. That means that all you are left with is c and y because x and a disappear when x = 0.
y = ax^2 + c
Givens
x = 0y = 1/3Solution
1/3 = a(0)^2 + c
1/3 = 0 + c
c = 1/3
Second Given
x = - 3y = 82/3Second Solution
82/3 = a*(-3)^2 + 1/3 Subtract 1/3 from both sides
82/3 - 1/3 = a*(9) + 1/3 - 1/3
81/3 = 9a Reduce the left
27 = 9a Divide by 9
27/9 = a
3 = a
Answer
y = 3x^2 + 1/3
the question and answers are below on the picture
Answer:
[tex]\large\boxed{B)\ 16x^2-25}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ (a-b)(a+b)=a^2-b^2[/tex]
[tex](4x-5)(4x+5)=(4x)^2-5^2=16x^2-25[/tex]
please help me out...........
Answer:
N(c, b)Step-by-step explanation:
If N is midpoint between Q and R, then use the formula of a midpoint:
[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
We have the points Q(0, 2b) and R(2c, 0). Substitute:
[tex]x=\dfrac{0+2c}{2}=\dfrac{2c}{2}=c\\\\y=\dfrac{2b+0}{2}=\dfrac{2b}{2}=b[/tex]
Solve the equation. Round to the nearest hundredth. Show work.
[tex]8^{-x+7} = 3^{7x+2}[/tex]
Answer:
Final answer is approx x=1.27.
Step-by-step explanation:
Given equation is [tex]8^{-x+7}=3^{7x+2}[/tex].
Now we need to solve equation [tex]8^{-x+7}=3^{7x+2}[/tex] and round to the nearest hundredth.
[tex]8^{-x+7}=3^{7x+2}[/tex]
[tex]\log(8^{-x+7})=\log(3^{7x+2})[/tex]
[tex]\left(-x+7\right)\cdot\log\left(8\right)=\left(7x+2\right)\cdot\log\left(3\right)[/tex]
[tex]-x\cdot\log\left(8\right)+7\cdot\log\left(8\right)=7x\cdot\log\left(3\right)+2\cdot\log\left(3\right)[/tex]
[tex]-x\cdot\log\left(8\right)-7x\cdot\log\left(3\right)=2\cdot\log\left(3\right)-7\cdot\log\left(8\right)[/tex]
[tex]x\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)=\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)[/tex]
[tex]x=\frac{\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)}{\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)}[/tex]
Now use calculator to calculate log values, we get:
[tex]x=1.26501646392[/tex]
Round to the nearest hundredth.
Hence final answer is approx x=1.27.
A counterexample for the expression sin y tan y= cos y is 0.
Answer:
True
Step-by-step explanation:
To answer this question we must evaluate
y = 0° on both sides of the equation.
For the left side we have:
[tex]sin(0\°) tan(0\°)[/tex]
We know that [tex]tan(0\°) =\frac{sin(0\°)}{cos(0\°)}[/tex]
We know that [tex]cos(0\°) = 1[/tex] and [tex]sin(0\°) = 0[/tex].
Therefore [tex]tan(0\°) = 0[/tex].
Then the left-hand side of the equals is equal to zero.
On the right side we have:
[tex]cos(y)[/tex]
When evaluating [tex]cos(y)[/tex] at [tex]y = 0[/tex]
We have to [tex]cos(0\°) = 1[/tex].
0 ≠ 1
The equation is not satisfied. Therefore y = 0 ° is a counterexample to the equation
Answer:true
Step-by-step explanation:
edge
Which expression is equivalent to 56 + 21? 7(49 + 14) 8(7 + 21) 8(48 + 13) 7(8 + 3)
Answer:
d 7(8 + 3)
Step-by-step explanation:
If cos x = 2 / 3 and x is in quadrant 4, find:
a. sin(x / 2)
b. cos(x / 2)
c. tan(x / 2)
Answer:
A
Step-by-step explanation:
cos(x)=2/3 in Q 4
sin(x/2)=+√(1-cos(x))/2
√(1-cos(x))/2=√(1-[2/3]/2=√(1/3)/2=-√(1/6) because sin is negative in Q 4
Answer:
See below.
Step-by-step explanation:
Because cos x = 2/3 the adjacent side = 2 and hypotenuse = 3 so the length of the opposite side =
√(3^2 - 2^2) = -√5 (its negative because we are in Quadrant 4).
So sin x = -√5/3.
(a) sin (x /2) = - √ [ (1 - cos x)/2 ]
= -√(1 - 2/3)/ 2)
= -√(1/6). or -0.4082.
(b) cos (x/2) = √ [ (1 + cos x)/2]
= √ 5/6 or 0.9129.
(c) tan (x /2) = ( 1 - cos x) / sin x.
= ( 1 - 2/3) / -√5/3
= -0.4472.
5x=-15x+3000 simplify step by step
The answer is 150 to this question
An artist wants to paint a mural. She mixes blue paint and red paint to make paint that is a certain shade of purple. The ratio of blue paint to red paint should be 3 to 2. She needs 20 gallons of the purple paint. How much more blue paint than red paint does she need?
Answer:
She needs 4 more gallons of blue paint than red paint
Step-by-step explanation:
Since the ratio is 3 to 2, 3 + 2 = 5.
The artist needs 20 gallons of purple paint, so 20/5 = 4
The amount of blue and red paint needed is 4x3 to 4x2, or 12 to 8.
She needs 12 gallons of blue paint and 8 gallons of red paint.
12 - 8 = 4
She needs 4 more gallons of blue paint than red paint.
Answer:
ok!
Step-by-step explanation:
blue = 8 gallons
red = 12 gallons
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 2x + 4), [−2, 2] Step 1 The absolute maximum and absolute minimum values of the function f occur either at a critical number or at an endpoint of the interval. Recall that a critical number is a value of x where f '(x) = 0 or where f '(x) doesn't exist. We begin by finding the critical numbers. f '(x) =
[tex]f(x)=\ln(x^2+2x+4)\implies f'(x)=\dfrac{2x+2}{x^2+2x+4}[/tex]
The numerator determines where the derivative vanishes (the denominator has a minimum value of 3, since [tex]x^2+2x+4=(x+1)^2+3\ge3[/tex]).
[tex]2x+2=0\implies x=-1[/tex]
At this critical point, we have
[tex]f(-1)=\ln((-1)^2+2(-1)+4)=\ln3\approx1.099[/tex]
At the endpoints, we have
[tex]f(-2)=\ln4\approx1.386[/tex]
[tex]f(2)=\ln12\approx2.485[/tex]
so [tex]f[/tex] attains a maximum value of [tex]\ln12[/tex] and a minimum value of [tex]\ln3[/tex].
The absolute minimum of the function f(x) = ln(x2 + 2x + 4) is at x=-2 where the value is ln(4) and the absolute maximum is at x=2 where the value is ln(8). There are no critical numbers within the selected interval.
Explanation:The given function is
f(x) = ln(x
2
+ 2x + 4)
, for which we need to find the absolute maximum and minimum in the interval [-2, 2]. Firstly, we find the derivative of the function:
f '(x) = (2x + 2) / (x
2
+ 2x + 4)
. To find the critical points, we set the derivative equal to zero and solve for x, finding no real solutions, indicating there are no critical numbers within the given interval. Thus, the extrema must occur at the endpoints. So, we find f(-2) = ln(4) and f(2) = ln(8).
The absolute minimum is ln(4) at x = -2 and the absolute maximum is ln(8) at x = 2
.
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Can someone help me with the First question ?
Answer:
Step-by-step explanation:
#1.
228 ÷ 6 = 38 in
#2.
186 ÷ 3 = 62 ft
#3.
360 ÷ 8 = 45 yd
#4.
119 ÷ 7 = 17 ft
I hope I helped you.
Answer:
Perimeter is the total outside dimension.
To find the length of one side, divide the total perimeter by the number of sides.
1. 228 / 6 = 38 inches.
2. 186 / 3 = 62 feet.
3. 360 / 8 = 45 yards
4. 119 / 7 = 17 feet.